Internal problem ID [13335]
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 (k).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-3 y^{3} x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x)=3*x*y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {-3 x^{2}+c_{1}}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {-3 x^{2}+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 44
DSolve[y'[x]==3*x*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {-3 x^2-2 c_1}} \\ y(x)\to \frac {1}{\sqrt {-3 x^2-2 c_1}} \\ y(x)\to 0 \\ \end{align*}