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Magazine Problem 32
Find the unique solution of the second-order initial value problem. $$y^{\prime \prime}+16 y=0, \quad y(0)=2, y^{\prime}(0)=-2$$
Problem 33
In Exercises solve the given differential equations (a) by variation of parameters and (b) by the method of undetermined coefficients. $$\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=e^{x}+e^{-x}$$
Problem 33
Find the unique solution of the second-order initial value problem. $$y^{\prime \prime}+12 y=0, \quad y(0)=0, y^{\prime}(0)=1$$
Problem 34
In Exercises solve the given differential equations (a) by variation of parameters and (b) by the method of undetermined coefficients. $$\frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}+4 y=2 e^{2 x}$$
Problem 34
Find the unique solution of the second-order initial value problem. $$12 y^{\prime \prime}+5 y^{\prime}-2 y=0, \quad y(0)=1, y^{\prime}(0)=-1$$
Problem 35
Find the unique solution of the second-order initial value problem. $$y^{\prime \prime}+8 y=0, \quad y(0)=-1, y^{\prime}(0)=2$$
Problem 35
In Exercises solve the given differential equations (a) by variation of parameters and (b) by the method of undetermined coefficients. $$\frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}-5 y=e^{x}+4$$
Problem 36
Find the unique solution of the second-order initial value problem. $$y^{\prime \prime}+4 y^{\prime}+4 y=0, \quad y(0)=0, y^{\prime}(0)=1$$
Problem 37
Find the unique solution of the second-order initial value problem. $$y^{\prime \prime}-4 y^{\prime}+4 y=0, \quad y(0)=1, y^{\prime}(0)=0$$
Problem 38
Find the unique solution of the second-order initial value problem. $$4 y^{\prime \prime}-4 y^{\prime}+y=0, \quad y(0)=4, y^{\prime}(0)=4$$
