38.2.26 problem 26

Internal problem ID [6455]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 26
Date solved : Wednesday, March 05, 2025 at 12:46:00 AM
CAS classification : [_linear]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1+x y \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 46

ode:=(-x^2+1)*diff(y(x),x) = 1+x*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\sqrt {x^{2}-1}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (x +1\right )}+\frac {c_1}{\sqrt {x -1}\, \sqrt {x +1}} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 32

ode=(1-x^2)*D[y[x],x]==1+x*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-\log \left (\sqrt {x^2-1}+x\right )+c_1}{\sqrt {x^2-1}} \]

✓ Sympy. Time used: 0.367 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + (1 - x**2)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - \log {\left (x + \sqrt {x^{2} - 1} \right )}}{\sqrt {x^{2} - 1}} \]