A. Solve each linear differential equation.

1. \(\displaystyle{\frac{dy}{dx}-2y=4+e^{3x}}\) View Solution
2. \(\displaystyle{x\frac{dy}{dx}- 4y=x^6e^x, \quad x \gt 0}\) View Solution
3. \( \displaystyle{(x+1)\frac{dy}{dx}+(x+2)y = 2xe^{-x}, \quad x \gt -1}\) View Solution
4. \( \displaystyle{\frac{dr}{d\theta}+r\sec \theta = \cos\theta}, \quad 0 < \theta < \pi/2 \) View Solution
5. \( \displaystyle{x^2y'+xy=1}, \quad x \gt 0 \) View Solution
6. \( \displaystyle{\frac{dy}{dt}+\frac{1}{t} y = \cos t}, \quad t \gt 0 \) View Solution
7. \( \displaystyle{\frac{dy}{dx}- (\sin x) y = 2 \sin x, \: y(\pi/2)=1}\) View Solution
8. \( \displaystyle{x\frac{dy}{dx}- y = x^2\,\sin x}, \quad x \gt 0 \) View Solution

B. Solve the following initial value problems (IVP).

1. \(\displaystyle{x\frac{dy}{dx}+2y=\frac{\sin x}{x}, \: y(\pi)=0, x \gt 0}\) View Solution
2. \( \displaystyle{\frac{dy}{dx}- (\sin x) y = 2 \sin x, \quad y(\pi/2)=1}\) View Solution