Internal problem ID [11215]
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 24. Equations solvable for \(p\). Page 49
Problem number: Ex 6.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 y^{2} x \right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(diff(y(x),x)^3-(2*x+y(x)^2)*diff(y(x),x)^2+(x^2-y(x)^2+2*x*y(x)^2)*diff(y(x),x)-(x^2-y(x)^2)*y(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1}{-x +c_{1}} y \left (x \right ) = -x -1+c_{1} {\mathrm e}^{x} y \left (x \right ) = x -1+{\mathrm e}^{-x} c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.276 (sec). Leaf size: 48
DSolve[(y'[x])^3-(2*x+y[x]^2)*(y'[x])^2+(x^2-y[x]^2+2*x*y[x]^2)*y'[x]-(x^2-y[x]^2)*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x+c_1} y(x)\to x+c_1 e^{-x}-1 y(x)\to -x+c_1 e^x-1 y(x)\to 0 \end{align*}