91Ó°ÊÓ

In Problems 49 and 50, use the substitution \(t=-x\) to solve the given initial- value problem on the interval \((-\infty, 0)\). $$ 4 x^{2} y^{\prime \prime}+y=0, y(-1)=2, y^{\prime}(-1)=4 $$

Use the substitution \(t=-x\) to solve the given initial-value problem on the interval \((-\infty, 0)\). $$ 4 x^{2} y^{\prime \prime}+y=0, y(-1)=2, y^{\prime}(-1)=4 $$

In Problems 49-58 find a homogeneous linear differential equation with constant coefficients whose general solution is given. $$ y \quad c_{1} e^{-5 x}+c_{2} e^{-4 x} $$

In Problems 49 and 50, use the substitution \(t=-x\) to solve the given initial- value problem on the interval \((-\infty, 0)\). $$ x^{2} y^{\prime \prime}-4 x y^{\prime}+6 y=0, y(-2)=8, y^{\prime}(-2)=0 $$

Use the substitution \(t=-x\) to solve the given initial-value problem on the interval \((-\infty, 0)\). $$ x^{2} y^{\prime \prime}-4 x y^{\prime}+6 y=0, y(-2)=8, y^{\prime}(-2)=0 $$

Find a homogeneous linear differential equation with constant coefficients whose general solution is given. $$ y \quad c_{1} e^{-5 x}+c_{2} e^{-4 x} $$

In Problems 49-58 find a homogeneous linear differential equation with constant coefficients whose general solution is given. $$ y \quad c_{1}+c_{2} e^{3 x} $$

Find a homogeneous linear differential equation with constant coefficients whose general solution is given. $$ y \quad c_{1}+c_{2} e^{3 x} $$

Find the steady-state current in an \(L R C\) -series circuit when \(L=\frac{1}{2} \mathrm{~h}, R=20 \Omega, C=0.001 \mathrm{f}\), and \(E(t)=100 \sin 60 t+\) \(200 \cos 40 t \mathrm{~V}\)

In Problems 49-58 find a homogeneous linear differential equation with constant coefficients whose general solution is given. $$ y \quad c_{1} e^{-10 x}+c_{2} x e^{-10 x} $$