Internal problem ID [4271]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1050.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 y^{2} x \right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}=0} \]
✓ 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}{c_{1} -x} y \left (x \right ) = c_{1} {\mathrm e}^{x}-x -1 y \left (x \right ) = x -1+c_{1} {\mathrm e}^{-x} \end{align*}
✓ Solution by Mathematica
Time used: 0.153 (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*}