MAT 275

TEST 1 (REVIEW)

Name:

ASU-ID:

I. Solve the following initial value problems.

1. $\frac{dy}{dt} = \sin(t) \cdot \sin(y)$ and $y(0) = \frac{\pi}{2} .$

2. $\frac{dy}{dt} = \frac{y }{ t + 3y }\;\;\;y(-1) = 0 .$

3.

$$\frac{dy}{dt} = \cos(t) \cdot y + \sin(2t)\sin(t) \;\;y(0)=0 .$$

II. Find the general solution for the Bernoulli equation

$$\frac{dy}{dt} = -\frac{1}{t}y + y^2$$

III. Find the general solution for the Ricatti equation

$$\frac{dy}{dt} = 4 -16t^2 + 8 yt - y^2.$$

Verify that $u(t)=4t$ is its particular solution.

IV. Find the general solution for

$$\frac{d^2y}{dt^2} + y = \cos(2t)$$

V. Find the general solution for

$$\frac{d^2y}{dt^2} +3\frac{dy}{dt} + 2y = 0$$