29.12.5 problem 324

Internal problem ID [4924]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 324
Date solved : Monday, January 27, 2025 at 09:51:24 AM
CAS classification : [_separable]

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }&=c y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

dsolve((x-a)*(x-b)*diff(y(x),x) = c*y(x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.445 (sec). Leaf size: 44

DSolve[(x-a)(x-b)D[y[x],x]==c y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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