28.15 problem 813

Internal problem ID [3544]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 28
Problem number: 813.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-2 \left (x -y\right ) y^{\prime }-4 y x=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve(diff(y(x),x)^2-2*(x-y(x))*diff(y(x),x)-4*x*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \relax (x ) = x^{2}+c_{1} \\ y \relax (x ) = c_{1} {\mathrm e}^{-2 x} \\ \end{align*}

Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 28

DSolve[(y'[x])^2-2(x-y[x])y'[x]-4 x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-2 x} \\ y(x)\to x^2+c_1 \\ y(x)\to 0 \\ \end{align*}