25.1.17 problem 17

Internal problem ID [4229]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 17
Date solved : Tuesday, March 04, 2025 at 05:56:58 PM
CAS classification : [_quadrature]

\begin{align*} \left (x^{3}+1\right ) y^{\prime }&=3 x^{2} \tan \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=\frac {\pi }{2} \end{align*}

✓ Maple. Time used: 0.884 (sec). Leaf size: 37

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

\[ y \left (x \right ) = 3 \left (\int _{0}^{x}\frac {\tan \left (\textit {\_z1} \right ) \textit {\_z1}^{2}}{\left (\textit {\_z1} +1\right ) \left (\textit {\_z1}^{2}-\textit {\_z1} +1\right )}d \textit {\_z1} \right )+\frac {\pi }{2} \]

✓ Mathematica. Time used: 8.694 (sec). Leaf size: 35

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

\[ y(x)\to \int _0^x\frac {3 K[1]^2 \tan (K[1])}{K[1]^3+1}dK[1]+\frac {\pi }{2} \]

✓ Sympy. Time used: 0.485 (sec). Leaf size: 41

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

\[ y{\left (x \right )} = - 3 \int \limits ^{0} \frac {x^{2} \tan {\left (x \right )}}{x^{3} + 1}\, dx + 3 \int \frac {x^{2} \tan {\left (x \right )}}{\left (x + 1\right ) \left (x^{2} - x + 1\right )}\, dx + \frac {\pi }{2} \]