15.7.10 problem 10

Internal problem ID [2991]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 10
Date solved : Sunday, March 30, 2025 at 01:03:54 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }-x y&=\frac {x}{y} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {{\mathrm e}^{x^{2}} c_1 -1} \\ y &= -\sqrt {{\mathrm e}^{x^{2}} c_1 -1} \\ \end{align*}

✓ Mathematica. Time used: 7.031 (sec). Leaf size: 57

ode=D[y[x],x]-x*y[x]==x/y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {-1+e^{x^2+2 c_1}} \\ y(x)\to \sqrt {-1+e^{x^2+2 c_1}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}

✓ Sympy. Time used: 0.422 (sec). Leaf size: 29

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

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