Internal problem ID [12973]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 3. Some basics about First order equations. Additional exercises. page
63
Problem number: 3.4 f.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{3}-25 y+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(y(x)^3-25*y(x)+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = -\frac {5}{\sqrt {25 \,{\mathrm e}^{-50 x} c_{1} +1}} y = \frac {5}{\sqrt {25 \,{\mathrm e}^{-50 x} c_{1} +1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.68 (sec). Leaf size: 110
DSolve[y[x]^3-25*y[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {5 e^{25 x}}{\sqrt {e^{50 x}+e^{50 c_1}}} y(x)\to \frac {5 e^{25 x}}{\sqrt {e^{50 x}+e^{50 c_1}}} y(x)\to -5 y(x)\to 0 y(x)\to 5 y(x)\to -\frac {5 e^{25 x}}{\sqrt {e^{50 x}}} y(x)\to \frac {5 e^{25 x}}{\sqrt {e^{50 x}}} \end{align*}