13. Intro to Differential Equations

Find the particular solution to the differential equation $y^{\prime }=2e^t+4t$ given the initial condition $y\left(0\right)=1$.

Find the general solution to the differential equation $\frac{dy}{dx}=-2x+5x^2$.

Find the particular solution to the differential equation $y^{\prime }=2\sin x+3\cos x$ given the initial condition $y\left(0\right)=4$.