The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \right) = - 3$$ is where $${{{d^2}y} \over {d{x^2}}} = 3x - 2$$

Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$

The differential equation $${{dy} \over {dx}} + py = Q,$$ is a linear equation of first order only if,

Solve $${{{d^4}v} \over {d{x^4}}} + 4{\lambda ^4}v = 1 + x + {x^2}$$