Internal problem ID [15089]
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: 201.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-2 y^{\prime } x=8 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x)^2-2*x*diff(y(x),x)-8*x^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 2 x^{2}+c_{1} \\ y \left (x \right ) &= -x^{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 25
DSolve[y'[x]^2-2*x*y'[x]-8*x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^2+c_1 \\ y(x)\to 2 x^2+c_1 \\ \end{align*}