64.6.7 problem 7

Internal problem ID [13278]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 7
Date solved : Wednesday, March 05, 2025 at 09:33:08 PM
CAS classification : [_separable]

\begin{align*} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=8*x^3*y(x)-12*x^3+(x^4+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3}{2}+\frac {c_{1}}{\left (x^{4}+1\right )^{2}} \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 38

ode=(8*x^3*y[x]-12*x^3)+(1+x^4)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {3 x^8+6 x^4+2 c_1}{2 \left (x^4+1\right )^2} \\ y(x)\to \frac {3}{2} \\ \end{align*}

✓ Sympy. Time used: 0.330 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x**3*y(x) - 12*x**3 + (x**4 + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{2 \left (x^{8} + 2 x^{4} + 1\right )} + \frac {3}{2} \]