### Solving Differential Equations

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- Solve the differential equation with initial conditions \(y'(0) = 0, y(1) = 0\) $$\frac{d}{dx^{2}}y(x)+\frac{d}{dx}y(x)=2y(x)$$
- Solve the differential equation $$\frac{d}{dx}v(x)+v(x)=2v^{2}\left(x\right)$$
- Solve the differential equation $$y''+y'=x+y$$
- Solve the differential equation $$y'(x)=\sin (x)$$
- Solve the differential equation $$2ydx-(2-x)dy=0$$