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 : Monday, January 27, 2025 at 08:43:08 AM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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