12.5.38 problem 35(a)

Internal problem ID [1662]
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 : 35(a)
Date solved : Saturday, March 29, 2025 at 11:21:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Maple. Time used: 0.373 (sec). Leaf size: 21

ode:=x^2*diff(y(x),x) = y(x)^2+x*y(x)-4*x^2; 
ic:=y(-1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {-2 x^{5}+2 x}{x^{4}+1} \]

✓ Mathematica. Time used: 2.11 (sec). Leaf size: 20

ode=x^2*D[y[x],x]==y[x]^2+x*y[x]-4*x^2; 
ic=y[-1]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {2 x \left (x^4-1\right )}{x^4+1} \]

✓ Sympy. Time used: 0.294 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + 4*x**2 - x*y(x) - y(x)**2,0) 
ics = {y(-1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 x \left (1 - x^{4}\right )}{x^{4} + 1} \]