60.1.2 problem 2

Internal problem ID [10016]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 2
Date solved : Monday, January 27, 2025 at 06:18:20 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+a y-c \,{\mathrm e}^{b x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

dsolve(diff(y(x),x) + a*y(x) - c*exp(b*x)=0,y(x), singsol=all)
 

\[ y = \frac {\left (c \,{\mathrm e}^{x \left (a +b \right )}+c_{1} \left (a +b \right )\right ) {\mathrm e}^{-a x}}{a +b} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 33

DSolve[D[y[x],x]+ a*y[x] - c*Exp[b*x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-a x} \left (c e^{x (a+b)}+c_1 (a+b)\right )}{a+b} \]