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Differential Equations. Verification Examples. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB. Verify that the given function satisfies the differential equation. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.

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differential equations

Differential Equations

Verification Examples

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide2

Verify that the given function satisfies the differential equation.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide3

Verify that the given function satisfies the differential equation.

First compute the derivative:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide4

Verify that the given function satisfies the differential equation.

First compute the derivative:

Now substitute into the differential equation:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide5

Verify that the given function satisfies the differential equation.

First compute the derivative:

Now substitute into the differential equation:

This is true, so the equation is satisfied

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide6

Verify that the given function satisfies the differential equation,

and find a value for C that satisfies the given initial condition.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide7

Verify that the given function satisfies the differential equation,

and find a value for C that satisfies the given initial condition.

Find the derivative:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide8

Verify that the given function satisfies the differential equation,

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide9

Verify that the given function satisfies the differential equation,

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

This is true, so the equation is satisfied

Now we need to satisfy the initial condition.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide10

Verify that the given function satisfies the differential equation,

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

This is true, so the equation is satisfied

Now we need to satisfy the initial condition.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide11

Verify that the given function satisfies the differential equation,

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

This is true, so the equation is satisfied

Now we need to satisfy the initial condition.

Set this equal to -1

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide12

Verify that the given function satisfies the differential equation,

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

This is true, so the equation is satisfied

Now we need to satisfy the initial condition.

Set this equal to -1

Our final solution is thus

We will call this a particular solution because it matches with a particular initial condition.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB