64.3.10 problem 11

Internal problem ID [13210]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 11
Date solved : Monday, March 31, 2025 at 07:37:57 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x y-3+\left (x^{2}+4 y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.069 (sec). Leaf size: 22

ode:=2*x*y(x)-3+(x^2+4*y(x))*diff(y(x),x) = 0; 
ic:=y(1) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {x^{2}}{4}+\frac {\sqrt {x^{4}+24 x +56}}{4} \]

✓ Mathematica. Time used: 0.147 (sec). Leaf size: 27

ode=(2*x*y[x]-3)+(x^2+4*y[x])*D[y[x],x]==0; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} \left (\sqrt {x^4+24 x+56}-x^2\right ) \]

✗ Sympy

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

Timed Out