IXL - Solve higher-order initial value problems (Calculus practice)

Solve the initial value problem.

′′

–

′

(

)

(

)

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question

Solve the initial value problem.

′′

′

(

)

(

)

key idea

A differential equation is an equation that involves a function and one or more of its derivatives. A solution to a differential equation is a function that satisfies the equation.

If a differential equation is of the form

′′

(

)

you can find a general solution by integrating twice.

An initial value problem is a differential equation together with one or more initial conditions. The solution to an initial value problem is a particular solution to the differential equation that satisfies all initial conditions.

solution

To solve the initial value problem, you need to find a function

(

)

that satisfies the differential equation

′′

and the initial conditions

′

(

)

and

(

)

First, integrate the differential equation to find an expression for

′

′′

′

∫

You can use the initial condition

′

(

)

to find the value of

′

(

)

(

)

–

So,

′

–

Next, integrate to find an expression for

′

–

∫

(

–

)

–

Now, use the initial condition

(

)

to find the value of

(

)

(

)

–

(

)

–

The solution to the initial value problem is

–

$Confetti$

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V.1Solve first-order initial value problems

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