Internal problem ID [2692]
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]
\[ \boxed {\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )-2 \left (b -a \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 55
dsolve((x-a)*(x-b)*(diff(y(x),x)-sqrt(y(x)))=2*(b-a)*y(x),y(x), singsol=all)
\[ \frac {\left (-x +b \right ) \left (a -b \right ) \ln \left (x -b \right )+\left (2 a -2 x \right ) \sqrt {y \left (x \right )}-\left (x +2 c_{1} \right ) \left (-x +b \right )}{2 a -2 x} = 0 \]
✓ Solution by Mathematica
Time used: 0.478 (sec). Leaf size: 43
DSolve[(x-a)*(x-b)*(y'[x]-Sqrt[y[x]])==2*(b-a)*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {(b-x)^2 ((b-a) \log (x-b)+x+2 c_1){}^2}{4 (a-x)^2} \]