# Complex numbers and ODEs: problem set 2 (basic solution techniques for ODEs)

## 3. Solving first order ODEs

(iv) Solve $xy y' - y^2 = (x + y)^2 e^{-y/x}$

Spoiler

(viii) Solve $\frac{dx}{dy} = \cos(2y) - x\cot y$

Spoiler

## 4. Solving a nonlinear ODE

We wish to solve $y' + ky = y^n \sin x.$

Spoiler

## 5. Solving an exact ODE

We wish to solve $\frac{dy}{dx} = \frac{(3x^2 + 2xy + y^2) \sin x + (6x + 2y)\cos x}{(2x + 2y)\cos x}.$

Spoiler