Internal problem ID [7781]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 201.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {2 f \relax (x ) y^{\prime }+2 f \relax (x ) y^{2}-f^{\prime }\relax (x ) y-2 f \relax (x )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 23
dsolve(2*f(x)*diff(y(x),x)+2*f(x)*y(x)^2-diff(f(x),x)*y(x)-2*f(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = i \tan \left (-i \left (\int \sqrt {f \relax (x )}d x \right )+c_{1}\right ) \sqrt {f \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.28 (sec). Leaf size: 39
DSolve[2*f[x]*y'[x]+2*f[x]*y[x]^2-f'[x]*y[x]-2*f[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to i \sqrt {f(x)} \tan \left (i \int _1^x-\sqrt {f(K[1])}dK[1]+c_1\right ) \\ \end{align*}