62.12.12 problem Ex 13

Internal problem ID [12787]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 13
Date solved : Monday, March 31, 2025 at 07:07:29 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 56

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

\[ y = \left (\int \frac {{\mathrm e}^{\frac {x}{\sqrt {-x^{2}+1}}} \left (x +\sqrt {-x^{2}+1}\right )}{\left (x -1\right )^{2} \left (x +1\right )^{2}}d x +c_1 \right ) {\mathrm e}^{-\frac {x}{\sqrt {-x^{2}+1}}} \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 38

ode=D[y[x],x]+y[x]/(1-x^2)^(3/2)== (x+(1-x^2)^(1/2))/(1-x^2)^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x + sqrt(1 - x**2))/(1 - x**2)**2 + y(x)/(1 - x**2)**(3/2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out