6.9.48 problem 39 part(f)

Internal problem ID [1804]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 39 part(f)
Date solved : Tuesday, September 30, 2025 at 05:19:40 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )-7 x y+7&=0 \end{align*}

✓ Maple. Time used: 0.166 (sec). Leaf size: 24

ode:=x^2*(diff(y(x),x)+y(x)^2)-7*x*y(x)+7 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-7 x^{6}+c_1}{x \left (-x^{6}+c_1 \right )} \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 34

ode=x^2*(D[y[x],x]+y[x]^2)-7*x*y[x]+7==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {7 x^6-6 c_1}{x^7-6 c_1 x}\\ y(x)&\to \frac {1}{x} \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(y(x)**2 + Derivative(y(x), x)) - 7*x*y(x) + 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {- 3 i \tan {\left (C_{1} + 3 i \log {\left (x \right )} \right )} + 4}{x} \]