60.1.10 problem 10

Internal problem ID [10024]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 10
Date solved : Monday, January 27, 2025 at 06:18:38 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+f^{\prime }\left (x \right ) y-f \left (x \right ) f^{\prime }\left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (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)
 

\[ y = f-1+{\mathrm e}^{-f} c_{1} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 60

DSolve[D[y[x],x] + D[ f[x],x]*y[x] - f[x]*D[ f[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x-f''(K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}-f''(K[1])dK[1]\right ) f(K[2]) f''(K[2])dK[2]+c_1\right ) \]