QUESTION

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1. (a) Verify that $y_{1}=e^{2 x}$ and $y_{2}=e^{5 x}$ are solutions of \[ y^{\prime \prime}-7 y^{\prime}+10 y=0 \] \[ \text { on }(-\infty, \infty) \text {. } \] (b) Verify that if $c_{1}$ and $c_{2}$ are arbitrary constants then $y=c_{1} e^{2 x}+c_{2} e^{5 x}$ is a solution of (A) on $(-\infty, \infty)$. (c) Solve the initial value problem \[ y^{\prime \prime}-7 y^{\prime}+10 y=0, \quad y(0)=-1, \quad y^{\prime}(0)=1 . \] (d) Solve the initial value problem \[ y^{\prime \prime}-7 y^{\prime}+10 y=0, \quad y(0)=k_{0}, \quad y^{\prime}(0)=k_{1} . \]

Public Answer

RYQZ4I The First Answerer