Internal problem ID [8158]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 578.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime }-2 x -F \left (-x^{2}+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 22
dsolve(diff(y(x),x) = 2*x+F(y(x)-x^2),y(x), singsol=all)
\[ y \relax (x ) = x^{2}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 100
DSolve[y'[x] == 2*x + F[-x^2 + y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}-\frac {F\left (K[2]-x^2\right ) \int _1^x-\frac {2 K[1] F'\left (K[2]-K[1]^2\right )}{F\left (K[2]-K[1]^2\right )^2}dK[1]+1}{F\left (K[2]-x^2\right )}dK[2]+\int _1^x\left (\frac {2 K[1]}{F\left (y(x)-K[1]^2\right )}+1\right )dK[1]=c_1,y(x)\right ] \]