Internal problem ID [10215]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
28. Summary. Page 59
Problem number: Ex 5.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class C], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y-\left (y^{\prime }\right )^{2} \left (x +1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 99
dsolve(y(x)=diff(y(x),x)^2*(x+1),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {\left (x +1+\sqrt {x c_{1}+x +c_{1}+1}\right )^{2} x}{\left (1+x \right )^{2}}+\frac {\left (x +1+\sqrt {x c_{1}+x +c_{1}+1}\right )^{2}}{\left (1+x \right )^{2}} \\ y \relax (x ) = \frac {\left (-x -1+\sqrt {x c_{1}+x +c_{1}+1}\right )^{2} x}{\left (1+x \right )^{2}}+\frac {\left (-x -1+\sqrt {x c_{1}+x +c_{1}+1}\right )^{2}}{\left (1+x \right )^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 57
DSolve[y[x]==(y'[x])^2*(x+1),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*}