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Kuta Software - Infinite Calculus Name___________________________________
Separable Differential Equations Date________________Period____
Find the general solution of each differential equation.
dy dx = e
x − y
2)
dy dx = 1 sec 2 y
dy dx = xe
y
4)
dy dx = 2 x e
2 y
5)
dy dx = 2 y − 1 6) dy dx = 2 yx + yx
-1-
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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.
dy dx = 2 e
x − y
, y ( 1 )^ = ln ( 2 e + 1)
x
y
8)
dy dx
= xy^2 , y ( 2 )^ = −
x
y
9)
dy dx = 12 x
y , y ( 0 )^ = 2
x
y
10)
dy dx = − x y
, y ( 1 )^ = − 2
x
y
-2-
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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.
dy dx = 2 e
x − y
, y ( 1 )^ = ln ( 2 e + 1)
x
y
e
y
= 2 e
x
y = ln ( 2 e
x
8)
dy dx
= xy^2 , y ( 2 )^ = −
x
y
−
1 y = x^2 2
1 2 y = − 2 x^2 + 1
dy dx = 12 x
y , y ( 0 )^ = 2
x
y
ln y = 3 x^4 + ln 2
y = 2 e
3 x^4
10)
dy dx = − x y
, y ( 1 )^ = − 2
x
y
y
2
= − x^2 2
3 2 y = − − x
+ 3 , − 3 < x < 3
-2- Create your own worksheets like this one with (^) Infinite Calculus. Free trial available at KutaSoftware.com
