24.1.22 problem 5(c)

Internal problem ID [4211]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 5(c)
Date solved : Tuesday, March 04, 2025 at 05:56:09 PM
CAS classification : [_linear]

\begin{align*} \sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 60

ode:=((x+a)*(x+b))^(1/2)*(2*diff(y(x),x)-3)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {3 \left (\int \sqrt {2 a +2 b +4 x +4 \sqrt {\left (x +a \right ) \left (x +b \right )}}d x \right )+4 c_{1}}{2 \sqrt {2 a +2 b +4 x +4 \sqrt {\left (x +a \right ) \left (x +b \right )}}} \]

✓ Mathematica. Time used: 0.391 (sec). Leaf size: 115

ode=Sqrt[(x+a)*(x+b)]*(2*D[y[x],x]-3)+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (-\frac {\sqrt {a+x} \sqrt {b+x} \text {arctanh}\left (\frac {\sqrt {b+x}}{\sqrt {a+x}}\right )}{\sqrt {(a+x) (b+x)}}\right ) \left (\int _1^x\frac {3}{2} \exp \left (\frac {\text {arctanh}\left (\frac {\sqrt {b+K[1]}}{\sqrt {a+K[1]}}\right ) \sqrt {a+K[1]} \sqrt {b+K[1]}}{\sqrt {(a+K[1]) (b+K[1])}}\right )dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(sqrt((a + x)*(b + x))*(2*Derivative(y(x), x) - 3) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out