6.5.30 problem 27

Internal problem ID [1654]
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 : 27
Date solved : Tuesday, September 30, 2025 at 04:41:47 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x y y^{\prime }&=3 x^{2}+4 y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=\sqrt {3} \\ \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 15

ode:=x*y(x)*diff(y(x),x) = 3*x^2+4*y(x)^2; 
ic:=[y(1) = 3^(1/2)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sqrt {4 x^{6}-1}\, x \]

✓ Mathematica. Time used: 0.482 (sec). Leaf size: 18

ode=x*y[x]*D[y[x],x]==3*x^2+4*y[x]^2; 
ic=y[1]==Sqrt[3]; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \sqrt {4 x^6-1} \end{align*}

✓ Sympy. Time used: 0.266 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2 + x*y(x)*Derivative(y(x), x) - 4*y(x)**2,0) 
ics = {y(1): sqrt(3)} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \sqrt {4 x^{6} - 1} \]