Internal problem ID [4364]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x)-(2*y(x)+y(x)^2*exp(3*x))=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {5}{5 \,{\mathrm e}^{-2 x} c_{1}-{\mathrm e}^{3 x}} \]
✓ Solution by Mathematica
Time used: 0.342 (sec). Leaf size: 29
DSolve[y'[x]-(2*y[x]+y[x]^2*Exp[3*x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {5 e^{2 x}}{e^{5 x}-5 c_1} \\ y(x)\to 0 \\ \end{align*}