In Exercises 129–132 solve the initial value problem.
131. x dy - (y + √y)dx = 0, y(1) = 1

Solve the initial value problems in Exercises 55–58.

57. d²y/dx² = 2e^(−x),y(0) = 1,y′(0) = 0

Initial Value Problems

Solve the initial value problems in Exercises 71–90.

d²r/dt² = 2/t³; dr/dt|ₜ ₌ ₁ =1, r(1) = 1

Solve the initial value problems in Exercises 53–56 for y as a function of x.

√(x² - 9) (dy/dx) = 1, where x > 3, y(5) = ln 3

Solve the initial value problems in Exercises 53–56 for y as a function of x.

(x² + 1)² (dy/dx) = √(x² + 1), where y(0) = 1

Solve the initial value problems in Exercises 71–90.

y⁽⁴⁾ = −sin t + cos t;

y′′′(0) =7, y′′(0) = y′(0) = −1, y(0) = 0

Solve the following initial value problem:

$\frac{dy}{dx}=2x-5$; $y\left(0\right)=4$

Using the acceleration function below, find the velocity function, if the velocity is v = 5 at time t = 2.

$a\left(t\right)=-20$

Find the function $f\left(x\right)$ that satisfies the following differential equation.

$f^{\prime\prime}\left(x\right)=3x^2$; $f^{\prime}\left(0\right)=1$; $f\left(1\right)=3$