91Ó°ÊÓ

Find the general solution and also the singular solution, if it exists. $$ 5 p^{2}+3 x p-y=0. $$

Solve the equation and find a particular solution that satisfies the given boundary conditions. $$ x y^{\prime \prime}=y^{\prime}+x^{5} ; \text { when } x=1, y=\frac{1}{2}, y^{\prime}=1 $$

Solve the equation and find a particular solution that satisfies the given boundary conditions. $$ x y^{\prime \prime}+y^{\prime}+x=0 ; \text { when } x=2, y=-1, y^{\prime}=-\frac{1}{2} $$

Find the general solution and also the singular solution, if it exists. $$ p^{2}+3 x p-y=0. $$

Find the general solution and also the singular solution, if it exists. $$ y=x p+x^{3} p^{2}. $$

Solve the equation and find a particular solution that satisfies the given boundary conditions. $$ y^{\prime \prime}=x\left(y^{\prime}\right)^{2} ; \text { when } x=2, y=\frac{1}{4} \pi, y^{\prime}=-\frac{1}{4} $$

Solve the equation and find a particular solution that satisfies the given boundary conditions. $$ y^{\prime \prime}=x\left(y^{\prime}\right)^{2} ; \text { when } x=0, y=1, y^{\prime}=\frac{1}{2} $$

Solve the equation and find a particular solution that satisfies the given boundary conditions. $$ y^{\prime \prime}=-e^{-2 y} ; \text { when } x=3, y=0, y^{\prime}=1 $$

Solve the equation and find a particular solution that satisfies the given boundary conditions. $$ y^{\prime \prime}=-e^{-2 y} ; \text { when } x=3, y=0, y^{\prime}=-1 $$

Solve the equation and find a particular solution that satisfies the given boundary conditions. $$ 2 y^{\prime \prime}=\sin 2 y ; \text { when } x=0, y=\pi / 2, y^{\prime}=1 $$