29.8.28 problem 233

Internal problem ID [4833]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 233
Date solved : Monday, January 27, 2025 at 09:41:52 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.586 (sec). Leaf size: 32

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

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