Internal problem ID [8347]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+f^{\prime }\left (x \right ) y=f \left (x \right ) f^{\prime }\left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x) + diff(f(x),x)*y(x) - f(x)*diff(f(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = f \left (x \right )-1+{\mathrm e}^{-f \left (x \right )} c_{1} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 18
DSolve[y'[x] + f'[x]*y[x] - f[x]*f'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to f(x)+c_1 e^{-f(x)}-1 \]