Solving Initial Value Problems
Solve the initial value problems in Exercises 15–20.
dy/dt + 2y = 3, y(0) = 1

Solve the following initial value problem for u as a function of t:

du/dt + (k/m) u = 0 (k and m positive constants), u(0) = u₀

a. as a first-order linear equation.

State the order of the differential equation and indicate if it is linear or nonlinear. 

$y^{{}^{\prime \prime \prime }}+3xy=4\sqrt{x}$

State the order of the differential equation and indicate if it is linear or nonlinear. 

$\frac{d^{2}y}{d{x}^2}-\left(\frac{dy}{dx}\right)(1-x)=2$