18.1.7 problem Problem 14.5 (a)

Internal problem ID [3463]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.5 (a)
Date solved : Tuesday, March 04, 2025 at 04:40:17 PM
CAS classification : [_linear]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+4 x y&=\left (-x^{2}+1\right )^{{3}/{2}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 42

ode:=(-x^2+1)*diff(y(x),x)+4*x*y(x) = (-x^2+1)^(3/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = c_{1} x^{4}-x^{3} \sqrt {-x^{2}+1}-2 c_{1} x^{2}+x \sqrt {-x^{2}+1}+c_{1} \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 29

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*y(x) - (1 - x**2)**(3/2) + (1 - x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out