6.5.28 problem 25

Internal problem ID [1652]
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 : 25
Date solved : Tuesday, September 30, 2025 at 04:41:41 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {y^{2}-3 x y-5 x^{2}}{x^{2}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.211 (sec). Leaf size: 23

ode:=diff(y(x),x) = (y(x)^2-3*x*y(x)-5*x^2)/x^2; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {-2 x^{7}+5 x}{2 x^{6}+1} \]

✓ Mathematica. Time used: 1.79 (sec). Leaf size: 24

ode=D[y[x],x]==(y[x]^2-3*x*y[x]-5*x^2)/x^2; 
ic=y[1]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {5 x-2 x^7}{2 x^6+1} \end{align*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (-5*x**2 - 3*x*y(x) + y(x)**2)/x**2,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x \left (\frac {5}{2} - x^{6}\right )}{x^{6} + \frac {1}{2}} \]