30.2.16 problem 16

Internal problem ID [7444]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 04:35:32 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

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

\[ y = \frac {1+x}{\sqrt {-x^{2}+1}}+\frac {{\mathrm e}^{-x} \sqrt {1+x}\, c_1}{\sqrt {x -1}} \]

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 86

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

\begin{align*} y(x)&\to \exp \left (\int _1^x-\frac {K[1]^2}{K[1]^2-1}dK[1]\right ) \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}-\frac {K[1]^2}{K[1]^2-1}dK[1]\right ) \sqrt {1-K[2]^2}}{1-K[2]}dK[2]+c_1\right ) \end{align*}

✗ Sympy

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

Timed Out