Worksheet #1: First order linear differential equations
Solve the following differential equations. You may need to bust out your integration note card!
a) y' - 3y = e^x
b) y' - 2xy = x
c) y' + y = sin(e^x)
d) y' = x + 5y
e) y' + 4y = x
f) xy' + 2y = e^{x^2}, x > 0
g) x^2y' + 2xy = cos x, x > 0
Solve the following initial value problems.
a) y' + (cos x)y = cos x, y(0) = 2
b) y' + y = x + e^x, y(0) = 0
c) xy' = y + x^3 sin x, x > 0, y(pi) = 0
d) xy' - 3y = x^2, x > 0, y(1) = 0
e) y' - 2xy = 2xe^{x^2}, y(0) = 3
f) (1 + x^2)y' + 2xy = 3sqrt{x}, y(0) = 2