Internal problem ID [8570]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 990.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+F \relax (x ) \left (-y^{2}+2 x^{2} y+1-x^{4}\right )-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 46
dsolve(diff(y(x),x) = -F(x)*(-y(x)^2+2*x^2*y(x)+1-x^4)+2*x,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} c_{1} {\mathrm e}^{\int -2 F \relax (x )d x}-x^{2}+c_{1} {\mathrm e}^{\int -2 F \relax (x )d x}+1}{c_{1} {\mathrm e}^{\int -2 F \relax (x )d x}-1} \]
✓ Solution by Mathematica
Time used: 0.333 (sec). Leaf size: 67
DSolve[y'[x] == 2*x - F[x]*(1 - x^4 + 2*x^2*y[x] - y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\exp \left (\int _1^x2 F(K[5])dK[5]\right )}{-\int _1^x\exp \left (\int _1^{K[6]}2 F(K[5])dK[5]\right ) F(K[6])dK[6]+c_1}+x^2+1 \\ y(x)\to x^2+1 \\ \end{align*}