29.8.27 problem 232

Internal problem ID [4832]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 232
Date solved : Monday, January 27, 2025 at 09:41:50 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 30

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

\begin{align*} y(x)\to -\frac {b}{c}+c_1 (a+x)^c \\ y(x)\to -\frac {b}{c} \\ \end{align*}