14.4.28 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
:
Tuesday, September 30, 2025 at 06:53:42 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*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 55
ode:=(x-a)*(x-b)*(diff(y(x),x)-y(x)^(1/2)) = 2*(b-a)*y(x);
dsolve(ode,y(x), singsol=all);
\[
\frac {\left (-x +b \right ) \left (a -b \right ) \ln \left (x -b \right )+\left (2 a -2 x \right ) \sqrt {y}-\left (x +2 c_1 \right ) \left (-x +b \right )}{2 a -2 x} = 0
\]
✓ Mathematica. Time used: 0.351 (sec). Leaf size: 43
ode=(x-a)*(x-b)*(D[y[x],x]-Sqrt[y[x]])==2*(b-a)*y[x];
ic={};
DSolve[{ode,ic},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*}
✓ Sympy. Time used: 2.078 (sec). Leaf size: 352
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
y = Function("y")
ode = Eq((-a + x)*(-b + x)*(-sqrt(y(x)) + Derivative(y(x), x)) + (2*a - 2*b)*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = \frac {C_{1}^{2} b^{2} - 2 C_{1}^{2} b x + C_{1}^{2} x^{2} - C_{1} a b^{2} \log {\left (- b + x \right )} + 2 C_{1} a b x \log {\left (- b + x \right )} - C_{1} a x^{2} \log {\left (- b + x \right )} + C_{1} b^{3} \log {\left (- b + x \right )} - 2 C_{1} b^{2} x \log {\left (- b + x \right )} + C_{1} b^{2} x + C_{1} b x^{2} \log {\left (- b + x \right )} - 2 C_{1} b x^{2} + C_{1} x^{3} + \frac {a^{2} b^{2} \log {\left (- b + x \right )}^{2}}{4} - \frac {a^{2} b x \log {\left (- b + x \right )}^{2}}{2} + \frac {a^{2} x^{2} \log {\left (- b + x \right )}^{2}}{4} - \frac {a b^{3} \log {\left (- b + x \right )}^{2}}{2} + a b^{2} x \log {\left (- b + x \right )}^{2} - \frac {a b^{2} x \log {\left (- b + x \right )}}{2} - \frac {a b x^{2} \log {\left (- b + x \right )}^{2}}{2} + a b x^{2} \log {\left (- b + x \right )} - \frac {a x^{3} \log {\left (- b + x \right )}}{2} + \frac {b^{4} \log {\left (- b + x \right )}^{2}}{4} - \frac {b^{3} x \log {\left (- b + x \right )}^{2}}{2} + \frac {b^{3} x \log {\left (- b + x \right )}}{2} + \frac {b^{2} x^{2} \log {\left (- b + x \right )}^{2}}{4} - b^{2} x^{2} \log {\left (- b + x \right )} + \frac {b^{2} x^{2}}{4} + \frac {b x^{3} \log {\left (- b + x \right )}}{2} - \frac {b x^{3}}{2} + \frac {x^{4}}{4}}{a^{2} - 2 a x + x^{2}}
\]