13. Intro to Differential Equations

First-Order Linear Equations

Solve the differential equations in Exercises 1–14.

e²ˣy' + 2e²ˣ y = 2x

33–42. Solving initial value problems Solve the following initial value problems.

y'(x) = 4 sec² 2x, y(0) = 8

In Exercises 1–4, show that each function y=f(x) is a solution of the accompanying differential equation.

2. y' = y²

b. y = -1/(x+3)

In Exercises 1–22, solve the differential equation.

x dy + (3y - x⁻² cos x) dx = 0, x > 0