Internal problem ID [15095]
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: 207.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {{y^{\prime }}^{2}-4 y^{\prime } x +2 y=-2 x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 77
dsolve(diff(y(x),x)^2-4*x*diff(y(x),x)+2*y(x)+2*x^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x^{2} \\ y \left (x \right ) &= \frac {1}{2} x^{2}+c_{1} x -\frac {1}{2} c_{1}^{2} \\ y \left (x \right ) &= \frac {1}{2} x^{2}-c_{1} x -\frac {1}{2} c_{1}^{2} \\ y \left (x \right ) &= \frac {1}{2} x^{2}-c_{1} x -\frac {1}{2} c_{1}^{2} \\ y \left (x \right ) &= \frac {1}{2} x^{2}+c_{1} x -\frac {1}{2} c_{1}^{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]^2-4*x*y'[x]+2*y[x]+2*x^2==0,y[x],x,IncludeSingularSolutions -> True]
Timed out