20.4.28 problem Problem 44

Internal problem ID [3663]
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
Date solved : Monday, January 27, 2025 at 07:52:49 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (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: 0.570 (sec). Leaf size: 43

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

\[ y(x)\to \frac {(b-x)^2 ((b-a) \log (x-b)+x+2 c_1){}^2}{4 (a-x)^2} \]