\text { a) Solve the equation } \frac{d^{2} y}{d x^{2}}=1 \text {, subject to the conditions } y(0)=3, y^{\prime}(0)=1 \text {. } Solve the second order differential equations \text { I. } \quad \frac{d^{2} y}{d x^{2}}-12 \frac{d y}{d x}+36 y=0 \text { ii. } \quad \frac{d^{2} y}{d x^{2}}+9 y=0 \text { iii. } \quad \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}-3 y=0

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5