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Magazine Problem 41
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(2 y^{\prime \prime}-2 y^{\prime}+y=0, \quad y(0)=-1, y^{\prime}(0)=0\)
Problem 41
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime \prime}+y^{\prime \prime}=8 x^{2} $$
Problem 42
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}-2 y^{\prime}+y=x^{3}+4 x $$
Problem 42
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(y^{\prime \prime}-2 y^{\prime}+y=0, \quad y(0)=5, y^{\prime}(0)=10\)
Problem 43
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(y^{*}+y^{\prime}+2 y=0, \quad y(0)=y^{\prime}(0)=0\)
Problem 43
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}-y^{\prime}-12 y=e^{4 x} $$
Problem 44
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(4 y^{\prime \prime}-4 y^{\prime}-3 y=0, \quad y(0)=1, y^{\prime}(0)=5\)
Problem 45
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}-2 y^{\prime}-3 y=4 e^{1}-9 $$
Problem 45
In Problems \(37-52\) solve the given differential equation subject to the indicated initial conditions. \(y^{\prime \prime}-3 y^{\prime}+2 y=0, \quad y(1)=0, y^{\prime}(1)=1\)
Problem 46
Solve the given differential equation by undetermined coefficients. $$ y^{\prime \prime}+6 y^{\prime}+8 y=3 e^{-2 x}+2 x $$
