Internal problem ID [2559]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (x^{3}+1\right ) y^{\prime }-3 \tan \relax (x ) x^{2}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = \frac {\pi }{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 36
dsolve([(1+x^3)*diff(y(x),x)=3*x^2*tan(x),y(0) = 1/2*Pi],y(x), singsol=all)
\[ y \relax (x ) = 3 \left (\int _{0}^{x}\frac {\textit {\_z1}^{2} \tan \left (\textit {\_z1} \right )}{\left (\textit {\_z1} +1\right ) \left (\textit {\_z1}^{2}-\textit {\_z1} +1\right )}d \textit {\_z1} \right )+\frac {\pi }{2} \]
✓ Solution by Mathematica
Time used: 8.288 (sec). Leaf size: 35
DSolve[{(1+x^3)*y'[x]==3*x^2*Tan[x],y[0]==Pi/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \int _0^x\frac {3 K[1]^2 \tan (K[1])}{K[1]^3+1}dK[1]+\frac {\pi }{2} \\ \end{align*}