Internal problem ID [7616]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 35.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+f \relax (x ) \left (y^{2}+2 a y+b \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 45
dsolve(diff(y(x),x) + f(x)*(y(x)^2 + 2*a*y(x) +b)=0,y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (\left (\int f \relax (x )d x \right ) \sqrt {a^{2}-b}+c_{1} \sqrt {a^{2}-b}\right ) \sqrt {a^{2}-b}-a \]
✓ Solution by Mathematica
Time used: 0.272 (sec). Leaf size: 89
DSolve[y'[x] + f[x]*(y[x]^2 + 2*a*y[x] +b)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -a+\sqrt {b-a^2} \tan \left (\sqrt {b-a^2} \left (\int _1^x-f(K[1])dK[1]+c_1\right )\right ) \\ y(x)\to -\sqrt {a^2-b}-a \\ y(x)\to \sqrt {a^2-b}-a \\ \end{align*}