Math 277 01,

the course of Dr. Mihailovs

Midterm 1

September 18, 1998

  1. Solve $ y'=3x+2$ .

  2. Solve $ \frac{dy}{dx}=\frac{x}{y}$ .

  3. Solve the initial-value problem $ \frac{dy}{dx}=\frac{x}{y}$, $ y(0)=1$ .

  4. Evaluate $ e^{i\pi/6}$ .

  5. Evaluate $ \left( \frac{\sqrt{3}}{2}+\frac{1}{2} i\right)^{-6i}$ .

  6. Solve $ xy'+2y=\cos x$ .

  7. Solve the initial-value problem $ y'-2y=e^{3x}$, $ y(0)=1$ .

  8. Solve $ y''+y'-2y=0$ .

  9. Solve the initial-value problem $ y''+y'-2y=e^x$, $ y(0)=0$, $ y'(0)=1$.

Copyright © 1998 Aleksandrs Mihailovs