57.1.7 problem 7

Internal problem ID [8991]
Book : First order enumerated odes
Section : section 1
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:26:38 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 18

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

\[ y(x)\to -a (x+1)+c_1 e^x \]