Internal problem ID [45]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-3 x^{2} \left (1+y^{2}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 12
dsolve([diff(y(x),x) = 3*x^2*(1+y(x)^2),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \tan \left (x^{3}+\frac {\pi }{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 15
DSolve[{y'[x]== 3*x^2*(1+y[x]^2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (x^3+\frac {\pi }{4}\right ) \\ \end{align*}