Internal problem ID [2792]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-f \relax (x ) f^{\prime }\relax (x )-f^{\prime }\relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
dsolve(diff(y(x),x) = f(x)*diff(f(x),x)+diff(f(x),x)*y(x),y(x), singsol=all)
\[ y \relax (x ) = -f \relax (x )-1+{\mathrm e}^{f \relax (x )} c_{1} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 18
DSolve[y'[x]==f[x] f'[x] + f'[x] y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -f(x)+c_1 e^{f(x)}-1 \\ \end{align*}