57.1.15 problem 15

Internal problem ID [8999]
Book : First order enumerated odes
Section : section 1
Problem number : 15
Date solved : Monday, January 27, 2025 at 05:26:46 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} c y^{\prime }&=a x +y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(c*diff(y(x),x)=a*x+y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 22

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

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