Internal problem ID [7683]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 102.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }+x y^{2}-y-x^{3} a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x*diff(y(x),x) + x*y(x)^2 - y(x) - a*x^3=0,y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (\frac {\sqrt {a}\, x^{2}}{2}+c_{1} \sqrt {a}\right ) x \sqrt {a} \]
✓ Solution by Mathematica
Time used: 3.311 (sec). Leaf size: 30
DSolve[x*y'[x] + x*y[x]^2 - y[x] - a*x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {a} x \tanh \left (\frac {1}{2} \sqrt {a} \left (x^2+2 c_1\right )\right ) \\ \end{align*}