Internal problem ID [7615]
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]
\[ \boxed {y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 35
dsolve(diff(y(x),x) + f(x)*(y(x)^2 + 2*a*y(x) +b)=0,y(x), singsol=all)
\[ y \left (x \right ) = -a +\tanh \left (\sqrt {a^{2}-b}\, \left (\int f \left (x \right )d x +c_{1} \right )\right ) \sqrt {a^{2}-b} \]
✓ Solution by Mathematica
Time used: 0.246 (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*}