Internal problem ID [3310]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]
\[ \boxed {y^{\prime }+\left (2 x^{2}-y\right ) y=x \left (x^{3}+2\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x) = x*(x^3+2)-(2*x^2-y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{2}+x^{3}-1}{x +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 24
DSolve[y'[x]==x(2+x^3)-(2 x^2-y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+\frac {1}{-x+c_1} y(x)\to x^2 \end{align*}