35.8.9 problem 9

Internal problem ID [6216]
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
Date solved : Monday, January 27, 2025 at 01:48:16 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

\begin{align*} y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(y(x),x)-(2*y(x)+y(x)^2*exp(3*x))=0,y(x), singsol=all)
 

\[ y = -\frac {5 \,{\mathrm e}^{2 x}}{{\mathrm e}^{5 x}-5 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.235 (sec). Leaf size: 29

DSolve[D[y[x],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*}