6.5.4 problem Example 3(b)

Internal problem ID [1628]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : Example 3(b)
Date solved : Tuesday, September 30, 2025 at 04:40:49 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }&=y^{2}+x y-x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 19

ode:=x^2*diff(y(x),x) = y(x)^2+x*y(x)-x^2; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.297 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to -\frac {x \left (x^2+3\right )}{x^2-3} \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 15

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

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