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Magazine Problem 23
Use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}+2 y^{\prime}+y=0, \quad y(0)=1, \quad y^{\prime}(0)=1 $$
Problem 24
Use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-4 y^{\prime}+4 y=t^{3} e^{2 t}, \quad y(0)=0, \quad y^{\prime}(0)=0 $$
Problem 24
In Problems, use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-4 y^{\prime}+4 y=t^{3} e^{2 t}, \quad y(0)=0, \quad y^{\prime}(0)=0 $$
Problem 25
Use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-6 y^{\prime}+9 y=t, \quad y(0)=0, \quad y^{\prime}(0)=1 $$
Problem 25
In Problems, use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-6 y^{\prime}+9 y=t, \quad y(0)=0, \quad y^{\prime}(0)=1 $$
Problem 26
Use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-4 y^{\prime}+4 y=t^{3}, \quad y(0)=1, \quad y^{\prime}(0)=0 $$
Problem 26
In Problems, use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-4 y^{\prime}+4 y=t^{3}, \quad y(0)=1, \quad y^{\prime}(0)=0 $$
Problem 27
In Problems, use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-6 y^{\prime}+13 y=0, \quad y(0)=0, \quad y^{\prime}(0)=-3 $$
Problem 27
Use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-6 y^{\prime}+13 y=0, \quad y(0)=0, \quad y^{\prime}(0)=-3 $$
Problem 28
Use the Laplace transform to solve the given initial-value problem. $$ 2 y^{\prime \prime}+20 y^{\prime}+51 y=0, \quad y(0)=2, \quad y^{\prime}(0)=0 $$
