29.1.4 problem 3

Internal problem ID [4611]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 3
Date solved : Monday, January 27, 2025 at 09:26:14 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 28

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

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