Example 1: Solve the given initial value problem. \text { a) } y^{\prime}=x^{2} y \text { b) } y^{\prime \prime}=e^{2 x-5 y} \text { with the initial condition } y(0)=0

\text {. } \text { co } y \text { 'sex } y^{2} \text { with the intital condition } y\left(\frac{5}{2}\right)=\frac{1}{2} \text { d) } \frac{y^{\prime}}{x}=y^{2}+y \text { with the initial condition } y(0)=-2