60.1.11 problem 11

Internal problem ID [10025]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 11
Date solved : Monday, January 27, 2025 at 06:18:39 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x)  + f(x)*y(x) - g(x)=0,y(x), singsol=all)
 

\[ y = \left (\int g \left (x \right ) {\mathrm e}^{\int fd x}d x +c_{1} \right ) {\mathrm e}^{-\int fd x} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 51

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

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