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Magazine Problem 52
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(\frac{d^{4} y}{d x^{4}}-y=0, \quad y(0)=y^{\prime}(0)=y^{\prime \prime}(0)=0, y^{\prime \prime \prime}(0)=1\)
Problem 52
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}+2 y^{\prime}+y=x^{\prime} e^{-1} $$
Problem 53
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}-2 y^{\prime}+5 y=e^{x} \sin x $$
Problem 53
In Problems 53-56 solve the given differential equation subject to the indicated boundary conditions. \(y^{\prime \prime}-10 y^{\prime}+25 y=0, \quad y(0)=1, y(1)=0\)
Problem 54
In Problems 53-56 solve the given differential equation subject to the indicated boundary conditions. \(y^{*}+4 y=0, \quad y(0)=0, y(x)=0\)
Problem 55
Solve the given differential equation by undetermined coefficients. $$ y^{*}+25 y=20 \sin 5 x $$
Problem 56
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}+y=4 \cos x-\sin x $$
Problem 56
In Problems 53-56 solve the given differential equation subject to the indicated boundary conditions. \(y^{\prime \prime}-y=0, \quad y(0)=1, y^{\prime}(1)=0\)
Problem 57
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}+y^{\prime}+y=x \sin x $$
Problem 57
In Problems 57-60 use a computer either as an aid in solving the auxiliary equation or as a means of directly obtaining the general solution of the given differential equation. If you use a CAS to obtain the general solution, simplify the output and write the solution in terms of real functions. \(y^{\prime \prime \prime}-6 y^{\prime \prime}+2 y^{\prime}+y=0\)
