IXL - Verify solutions to differential equations (Calculus practice)

a solution to this differential equation?

–

′

yes

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Learn with an example

question

cos

–

sin

a solution to this differential equation?

′

–

cos

yes

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.

solution

The differential equation

′

–

cos

includes the functions

and

′

You are given

cos

–

sin

so first find

′

(

cos

–

sin

)

′

–

sin

–

cos

Now, substitute

and

′

into the differential equation to determine whether the function is a solution.

′

–

≟

–

cos

(

–

sin

–

cos

)

–

(

cos

–

sin

)

≟

–

cos

–

sin

–

cos

–

cos

sin

≟

–

cos

–

cos

–

cos

This equation is true for all

cos

–

sin

is a solution to the differential equation.

$Confetti$

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