(Solved): Can someone help me with this question? Thank you! 3. For the following initial value problems, fi ...

Can someone help me with this question?

Thank you!

3. For the following initial value problems, find a solution from the given family of general solutions. \[ y^{\prime}=y . \] (a) (3 points) \[ \left\{\begin{array}{l} \frac{\mathrm{d} y}{\mathrm{~d} x}=5 y \\ y(1)=8 \end{array}\right. \] Family of solutions: \( y(x)=C e^{5 x} \) (b) (5 points) \[ \left\{\begin{array}{l} \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}-5 \frac{\mathrm{d} y}{\mathrm{~d} x}+4 y=0 \\ y(0)=4, y^{\prime}(0)=2 \end{array}\right. \] Family of solutions: \( y(x)=C_{1} e^{x}+C_{2} e^{4 x} \)