57.1.8 problem 8

Internal problem ID [8992]
Book : First order enumerated odes
Section : section 1
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:26:39 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

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

\[ y = \frac {{\mathrm e}^{b x} c_{1} b^{2}-a x b -a}{b^{2}} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 25

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

\[ y(x)\to -\frac {a b x+a}{b^2}+c_1 e^{b x} \]