30.6.18 problem 19

Internal problem ID [7553]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 19
Date solved : Tuesday, September 30, 2025 at 04:47:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=x^2-3*y(x)^2+2*x*y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {c_1 x +1}\, x \\ y &= -\sqrt {c_1 x +1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.156 (sec). Leaf size: 34

ode=(x^2-3*y[x]^2)+(2*x*y[x])*D[y[x],x]==0 ; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.232 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = - x \sqrt {C_{1} x + 1}, \ y{\left (x \right )} = x \sqrt {C_{1} x + 1}\right ] \]