85.24.1 problem 1

Internal problem ID [22578]
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. A Exercises at page 57
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:52:05 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {c_1 -\sqrt {c_1^{2}+4 x^{2}}}{2 x c_1} \\ y &= \frac {c_1 +\sqrt {c_1^{2}+4 x^{2}}}{2 x c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.327 (sec). Leaf size: 77

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

\begin{align*} y(x)&\to \frac {1-\sqrt {\frac {1}{x^2}} x \sqrt {1+4 c_1 x^2}}{2 x}\\ y(x)&\to \frac {1+\sqrt {\frac {1}{x^2}} x \sqrt {1+4 c_1 x^2}}{2 x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.505 (sec). Leaf size: 34

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

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