Internal problem ID [2819]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 64.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-1+x +x^{3}-y \left (1+2 x^{2}\right )+x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 61
dsolve(diff(y(x),x) = 1-x-x^3+(2*x^2+1)*y(x)-x*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (c_{1} x^{2}-c_{1} x +c_{1}\right ) {\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}}+{\mathrm e}^{\frac {x^{3}}{3}} x}{\left (c_{1} x -c_{1}\right ) {\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}}+{\mathrm e}^{\frac {x^{3}}{3}}} \]
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 39
DSolve[y'[x]==1-x-x^3+(1+2 x^2)y[x]-x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x ((x-1) x+1)+c_1 x}{e^x (x-1)+c_1} \\ y(x)\to x \\ \end{align*}