29.10.4 problem 270

Internal problem ID [4870]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 270
Date solved : Sunday, March 30, 2025 at 04:08:06 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 32

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

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

✓ Mathematica. Time used: 4.647 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 1.097 (sec). Leaf size: 36

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

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