Internal problem ID [13337]
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 (m).
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: 14
dsolve(diff(y(x),x)-3*x^2*y(x)^2=-3*x^2,y(x), singsol=all)
\[ y \left (x \right ) = -\tanh \left (x^{3}+3 c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.45 (sec). Leaf size: 44
DSolve[y'[x]-3*x^2*y[x]^2==-3*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1-e^{2 \left (x^3+c_1\right )}}{1+e^{2 \left (x^3+c_1\right )}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}