Internal problem ID [2183]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )-2 \left (-a +b \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 89
dsolve((x-a)*(x-b)*(diff(y(x),x)-sqrt(y(x)))=2*(b-a)*y(x),y(x), singsol=all)
\[ \sqrt {y \relax (x )}+\frac {b^{2}}{2 x -2 a}-\frac {x^{2}}{2 \left (x -a \right )}-\frac {\ln \left (-x +b \right ) \left (x -b \right ) b}{2 \left (x -a \right )}+\frac {a \ln \left (-x +b \right ) \left (x -b \right )}{2 x -2 a}-\frac {c_{1} \left (x -b \right )}{x -a} = 0 \]
✓ Solution by Mathematica
Time used: 0.5 (sec). Leaf size: 43
DSolve[(x-a)*(x-b)*(y'[x]-Sqrt[y[x]])==2*(b-a)*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(b-x)^2 ((b-a) \log (x-b)+x+2 c_1){}^2}{4 (a-x)^2} \\ \end{align*}