Internal problem ID [13338]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.7 (n).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-3 x^{2} y^{2}=3 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(diff(y(x),x)-3*x^2*y(x)^2=3*x^2,y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (x^{3}+3 c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 26
DSolve[y'[x]-3*x^2*y[x]^2==3*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (x^3+c_1\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}