Internal problem ID [3712]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 988.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x +y\right )^{2} \left (y^{\prime }\right )^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 48
dsolve((x+y(x))^2*diff(y(x),x)^2 = y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{\LambertW \left (x \,{\mathrm e}^{c_{1}}\right )-c_{1}} \\ y \relax (x ) = -x -\sqrt {x^{2}+2 c_{1}} \\ y \relax (x ) = -x +\sqrt {x^{2}+2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.475 (sec). Leaf size: 101
DSolve[(x+y[x])^2 (y'[x])^2==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {x^2+e^{2 c_1}} \\ y(x)\to -x+\sqrt {x^2+e^{2 c_1}} \\ y(x)\to \frac {x}{\text {ProductLog}\left (e^{-c_1} x\right )} \\ y(x)\to 0 \\ y(x)\to -\sqrt {x^2}-x \\ y(x)\to \sqrt {x^2}-x \\ \end{align*}