Internal problem ID [2322]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 9.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (y+x \right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve(diff(y(x),x)^3+(x+y(x)-2*x*y(x))*diff(y(x),x)^2-2*diff(y(x),x)*x*y(x)*(x+y(x))=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} {\mathrm e}^{x^{2}} y \left (x \right ) = -x +1+{\mathrm e}^{-x} c_{1} y \left (x \right ) = c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 36
DSolve[y'[x]^3+(x+y[x]-2*x*y[x])*y'[x]^2-2*y'[x]*x*y[x]*(x+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 y(x)\to c_1 e^{x^2} y(x)\to -x+c_1 e^{-x}+1 \end{align*}