4.2.35 problem 36

Internal problem ID [1163]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 36
Date solved : Tuesday, September 30, 2025 at 04:25:27 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2}+3 x y+y^{2}-x^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=x^2+3*x*y(x)+y(x)^2-x^2*diff(y(x),x) = 0; 
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: 0.088 (sec). Leaf size: 28

ode=(x^2+3*x*y[x]+y[x]^2)-x^2* D[y[x],x]==0; 
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: 0.141 (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)
 

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