85.25.1 problem 1

Internal problem ID [22586]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 57
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:53:36 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

\[ x y-\frac {\left (x^{2}+y^{2}\right )^{{3}/{2}}}{3}+c_1 = 0 \]

✓ Mathematica. Time used: 9.68 (sec). Leaf size: 319

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

\begin{align*} y(x)&\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,1\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,2\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,3\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,4\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,5\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,6\right ] \end{align*}

✗ Sympy

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

Timed Out