Internal problem ID [15091]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 203.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+y x=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)^2-(2*x+y(x))*diff(y(x),x)+x^2+x*y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2}}{2}+c_{1} \\ y \left (x \right ) &= -x -1+{\mathrm e}^{x} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 30
DSolve[y'[x]^2-(2*x+y[x])*y'[x]+x^2+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to -x+c_1 e^x-1 \\ \end{align*}