Exercise: 1) Find the general solution for the following equation i) $\frac{d^{2} y}{d x^{2}}+5 \frac{d y}{d x}+6 y=0$ ii) $\frac{d^{2} y}{d x^{2}}+4 \frac{d y}{d x}+4 y=0$ iii) $\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+4 y=0$ 2) Solve the following initial value problem i) $y^{\prime \prime}-2 y^{\prime}-3 y=0, \quad y()=2, \quad y^{\prime} (0)=14$ ii) $y^{\prime \prime}+2 y^{\prime}+y=0, \quad y()=4 \quad y^{\prime} (0)=-5$ iii) $10 y^{\prime \prime)-50 y^{\prime}-65 y=0, \quad y()=1.5 \quad y^{\prime} (0)=1.5$ iv) $y^{\prime \prime}-9 y=0, \quad y=-2, \quad y^{\prime} (0)=-12$CS.SD. 110