29.19.25 problem 538

Internal problem ID [5134]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 538
Date solved : Monday, January 27, 2025 at 10:13:47 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 37

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

\begin{align*} y(x)\to c_1 e^{\frac {a \log (a+x)-b \log (b+x)}{a-b}} \\ y(x)\to 0 \\ \end{align*}