08 - Intro Differential Equations.ks-ic - Kuta Software

Kuta Software - Infinite Calculus

Name___________________________________

Introduction to Differential Equations

Date________________ Period____

Find the general solution of each differential equation. 1)

dy = 2x + 2 dx

3)

1 dy =− 2 dx x

2) f ' ( x) = −2 x + 1

4)

1 dy = dx ( x + 3) 2

For each problem, find the particular solution of the differential equation that satisfies the initial condition. You may use a graphing calculator to sketch the solution on the provided graph. 5)

dy = −4 x + 1, y(−1) = −3 dx

6)

( )

2π dy = −2sin x, y =0 dx 3

y

−4

−3

−2

y

4

4

3

3

2

2

1

1

−1

1

2

3

4 x

−1

−π −

π 2

−1

−2

−2

−3

−3

−4

−4

©8 E2x0l1F3R BKxu4tBaa HSuoif2tgwBaprwez KLfLgCe.z g 4AZl1l5 QrBi0g4hxtish erQeFsherrivZeldv.K j MMXaHdZe1 1w9iltyhc dIdnAfbiRnriItheS OCbaKlzcGuElpumsv.T

π 2

π

x

Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Introduction to Differential Equations

Date________________ Period____

Find the general solution of each differential equation. 1)

2) f ' ( x) = −2 x + 1

dy = 2x + 2 dx

f ( x) = − x 2 + x + C

y = x2 + 2x + C

3)

1 dy =− 2 dx x y=

4)

1 +C x

1 dy = dx ( x + 3) 2 y=−

1 +C x+3

For each problem, find the particular solution of the differential equation that satisfies the initial condition. You may use a graphing calculator to sketch the solution on the provided graph. 5)

dy = −4 x + 1, y(−1) = −3 dx

6)

( )

2π dy = −2sin x, y =0 dx 3

y

−4

−3

−2

y

4

4

3

3

2

2

1

1

−1

1

2

3

4 x

−1

−π −

π 2

−1

−2

−2

−3

−3

−4

−4

y = −2 x 2 + x

π 2

π

x

y = 2cos x + 1

Create your own worksheets like this one with Infinite Calculus. Free trial available at KutaSoftware.com

©0 G2z011w3K oK8uQtBag MS3ogfnt0wDa4rCeu FLsL9Ci.U l 8AFlAlJ erkiggSh7tOsx 6rAeLsoecrbvEeadh.N Z oMUaCdpeD Kwbitt1hn UIHnzfLiMnpiDt3eT PCTa7lzc8uylQuLsr.p

Worksheet by Kuta Software LLC