a$).$ Show that $e^{4x}$ and $e^{-x}$ are linearly independent solutions of the ODE $y^{\text{'}\text{'}}-3y^{\text{'}}-4y=0$ and find the solution that satisfies the initial conditions y $(0)=1$ and $y^{\text{'}}(0)=2$

b$).$ Solve the differential equation $y^{\text{'}\text{'}}+x(y^{\text{'}}{)}^2=0$