2. Explain how you can convert the nth-order initial value problem \frac{d^{n} y}{d x^{n}}=f\left(x, \frac{d^{n-1} y}{d x^{n-1}}, \ldots, \frac{d^{2} y}{d x^{2}}, \frac{d y}{d x}, y\right) y=a_{0}, \frac{d y}{d x}=a_{1}, \frac{d^{2}

y}{d x^{2}}=a_{2}, \ldots, \frac{d^{n-1} y}{d x^{n-1}}=a_{n-1} at x = 0, into a system of n coupled first-order initial value problems. with into a set of two coupled first-order initial value problems. \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}-\frac{3}{4} y=0, \quad y(0)=1, \quad \frac{d y}{d x}(0)=2 Use a step length h = 0.25 to find numerical approximations to both y and y'at x = 0.5 using the generalization to two coupled equations of the third-order Runge-Kutta scheme k1= hf (Xn, Yn), k3=hf (Xn + h, yn – k1 + 2k2), k2= hf(xn + 1/2 h, yn + 1/2 K1), y_{n+1}=y_{n}+\frac{1}{6}\left(k_{1}+4 k_{2}+k_{3}\right) Find the exact solution to the differential equation, and comment on the errors in your estimates.[6 marks] Convert the initial value problem