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## Differential Equations

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### Differential Equations

Separable Examples

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

This C is really eC.

Since it is still arbitrary we can still call it C.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

This C is really eC.

Since it is still arbitrary we can still call it C.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

C is an arbitrary constant, so we can multiply by -2 and still call it C

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

C is an arbitrary constant, so we can multiply by -2 and still call it C

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Now we can find the constant from the initial value:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Now we can find the constant from the initial value:

Plugging this into our general solution we get

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Find C from the initial value

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Find C from the initial value

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

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