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Magazine Problem 46
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(y^{\prime \prime}+y=0, \quad y\left(\frac{\pi}{3}\right)=0, y^{\prime}\left(\frac{\pi}{3}\right)=2\)
Problem 47
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(y^{\prime \prime \prime}+12 y^{\prime \prime}+36 y^{\prime}=0, \quad y(0)=0, y^{\prime}(0)=1, y^{\prime \prime}(0)=-7\)
Problem 47
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}+25 y=6 \sin x $$
Problem 48
Solve the given differential equation by undetermined coefficients. $$ y^{*}+4 y=4 \cos x+3 \sin x-8 $$
Problem 49
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(y^{\prime \prime \prime}-8 y=0, \quad y(0)=0, y^{\prime}(0)=-1, y^{\prime \prime}(0)=0\)
Problem 49
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}+6 y^{\prime}+9 y=-x e^{4 x} $$
Problem 50
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}+3 y^{\prime}-10 y=x\left(e^{x}+1\right) $$
Problem 50
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(\frac{d^{4} y}{d x^{4}}=0, \quad y(0)=2, y^{\prime}(0)=3, y^{\prime \prime}(0)=4, y^{\prime \prime \prime}(0)=5\)
Problem 51
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}-y=x^{2} e^{x}+5 $$
Problem 51
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(\frac{d^{4} y}{d x^{4}}-3 \frac{d^{3} y}{d x^{3}}+3 \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0, \quad y(0)=y^{\prime}(0)=0, y^{\prime \prime}(0)=y^{\prime \prime \prime}(0)=1\)
