Internal problem ID [11229]
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]
\[ \boxed {y-{y^{\prime }}^{2} \left (1+x \right )=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 53
dsolve(y(x)=diff(y(x),x)^2*(x+1),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (x +1+\sqrt {\left (1+x \right ) \left (c_{1} +1\right )}\right )^{2}}{1+x} \\ y \left (x \right ) &= \frac {\left (-x -1+\sqrt {\left (1+x \right ) \left (c_{1} +1\right )}\right )^{2}}{1+x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.1 (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*}