Verify that \(y=Ce^{2x}\) solves \(dy/dx=2y\), where \(C\) is a constant.

Solve \(dy/dx=3x^2\).

Solve the initial value problem \(dy/dx=2x\), \(y(0)=5\).

Solve \(dy/dx=xy\) by separation of variables.

Solve \(dy/dx+y=0\).

Solve the linear differential equation \(dy/dx+2y=6\).

Solve \(dy/dx=x+y\) is not separable by simple algebra. State whether it is linear and identify \(P(x)\) and \(Q(x)\) in \(y'+P(x)y=Q(x)\).

Solve the initial value problem \(dy/dx=4y\), \(y(0)=2\).

Find the equilibrium solutions of \(dy/dt=y(3-y)\).

Use Euler's method with step size \(h=0.5\) for \(y'=x+y\), starting from \((x_0,y_0)=(0,1)\), to estimate \(y(1)\).