29.2.12 problem 37

Internal problem ID [4645]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 37
Date solved : Monday, January 27, 2025 at 09:29:17 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )+f^{\prime }\left (x \right ) y \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y \left (x \right ) = -f \left (x \right )-1+{\mathrm e}^{f \left (x \right )} c_{1} \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 18

DSolve[D[y[x],x]==f[x] D[ f[x],x] + D[ f[x],x] y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -f(x)+c_1 e^{f(x)}-1 \]