Internal problem ID [4113]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 876.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _dAlembert]
\[ \boxed {\left (x +1\right ) {y^{\prime }}^{2}-y=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 99
dsolve((1+x)*diff(y(x),x)^2 = y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \frac {\left (x +1+\sqrt {c_{1} x +c_{1} +x +1}\right )^{2} x}{\left (x +1\right )^{2}}+\frac {\left (x +1+\sqrt {c_{1} x +c_{1} +x +1}\right )^{2}}{\left (x +1\right )^{2}} y \left (x \right ) = \frac {\left (-x -1+\sqrt {c_{1} x +c_{1} +x +1}\right )^{2} x}{\left (x +1\right )^{2}}+\frac {\left (-x -1+\sqrt {c_{1} x +c_{1} +x +1}\right )^{2}}{\left (x +1\right )^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 57
DSolve[(1+x) (y'[x])^2==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} y(x)\to x+c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} y(x)\to 0 \end{align*}