57.1.16 problem 16

Internal problem ID [9000]
Book : First order enumerated odes
Section : section 1
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:26:48 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

\[ y = \frac {{\mathrm e}^{\frac {b x}{c}} c_{1} b^{2}-a \left (b x +c \right )}{b^{2}} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 28

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

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