20.4.11 problem Problem 19

Internal problem ID [3646]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 19
Date solved : Sunday, March 30, 2025 at 01:57:57 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }&=y^{2}+3 x y+x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=x^2*diff(y(x),x) = y(x)^2+3*x*y(x)+x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x \left (\ln \left (x \right )+c_1 +1\right )}{\ln \left (x \right )+c_1} \]

✓ Mathematica. Time used: 0.155 (sec). Leaf size: 28

ode=x^2*D[y[x],x]==y[x]^2+3*x*y[x]+x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {x (\log (x)+1+c_1)}{\log (x)+c_1} \\ y(x)\to -x \\ \end{align*}

✓ Sympy. Time used: 0.246 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = x \left (- 8 x^{2} - 1\right ) \]