(Solved):   Solve the following problem with the Euler method: \[ 2 \frac{d^{2} y}{d x^{2}}+3 \frac{d ...

 

Solve the following problem with the Euler method: \[ 2 \frac{d^{2} y}{d x^{2}}+3 \frac{d y}{d x}+3.125 y=\sin x \] where \( y(0)=5 \) and \( y^{\prime}(0)=3 \). Solve from \( x=0 \) to 5 with \( h=0.5 \). Find the error considering the exact solution is \[ y(x)=e^{-0.75 x}(5.292237 \cos x+6.859589 \sin x)-0.292237 \cos x+0.109589 \sin x \] Display the analytical and numerical results on the same graph.