Internal problem ID [2805]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-f \relax (x )-x f \relax (x ) y-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve(diff(y(x),x) = f(x)+x*f(x)*y(x)+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{\int \frac {f \relax (x ) x^{2}-2}{x}d x}}{c_{1}-\left (\int {\mathrm e}^{\int \frac {f \relax (x ) x^{2}-2}{x}d x}d x \right )}-\frac {1}{x} \]
✓ Solution by Mathematica
Time used: 0.601 (sec). Leaf size: 76
DSolve[y'[x]==f[x]+x f[x] y[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x+\frac {\exp \left (-\int _1^x-f(K[5]) K[5]dK[5]\right )}{\int _1^x\frac {\exp \left (-\int _1^{K[6]}-f(K[5]) K[5]dK[5]\right )}{K[6]^2}dK[6]+c_1}}{x^2} \\ y(x)\to -\frac {1}{x} \\ \end{align*}