29.8.24 problem 229

Internal problem ID [4829]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 229
Date solved : Monday, January 27, 2025 at 09:41:46 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

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

\[ y \left (x \right ) = b \left (x +a \right ) \ln \left (x +a \right )+\left (b +c_{1} \right ) a +c_{1} x \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 27

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

\[ y(x)\to (a+x) \left (-\frac {b x}{a+x}+b \log (a+x)+c_1\right ) \]