6.5.29 problem 26

Internal problem ID [1653]
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 : 26
Date solved : Tuesday, September 30, 2025 at 04:41:45 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

With initial conditions

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 21

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

\[ y = \frac {-4 x^{2}+3 x}{2 x -3} \]

✓ Mathematica. Time used: 0.268 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to -\frac {x (4 x-3)}{2 x-3} \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 15

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

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