Internal problem ID [3311]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]
\[ \boxed {y^{\prime }-\left (2 x^{2}-y\right ) y=1+x \left (-x^{3}+2\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(diff(y(x),x) = 1+x*(-x^3+2)+(2*x^2-y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2} {\mathrm e}^{-2 x} c_{1} -x^{2}-{\mathrm e}^{-2 x} c_{1} -1}{{\mathrm e}^{-2 x} c_{1} -1} \]
✓ Solution by Mathematica
Time used: 0.141 (sec). Leaf size: 34
DSolve[y'[x]==1+x(2-x^3)+(2 x^2-y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2-\frac {2}{1+2 c_1 e^{2 x}}+1 y(x)\to x^2+1 \end{align*}