$($a$)$ Solve the following equation using Galekin's method $($Use at least a two$-$parameter

solution$)$

$\frac{dy}{(d)x}=50(1+cosx)-0\mathrm{.}05y,0x2$

for boundary condition $y(0)=200.$

$($b$)$ Explain the principle of Rayleigh$-$Ritz method. Solve the following equation by

Rayleigh$-$Ritz method.

$-y^{\text{'}\text{'}}+{}^{2}y=2{}^2(sinx),0x1$

for boundary conditions $y(0)=0$ and $y(1)=0.$