35.4.16 problem 25 part (c)

Internal problem ID [6134]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 25 part (c)
Date solved : Monday, January 27, 2025 at 01:38:02 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Riccati]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

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

\[ y = i \tan \left (i x +c_1 \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.288 (sec). Leaf size: 19

DSolve[D[y[x],x]== Exp[-x]*y[x]^2+y[x]-Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -e^x \tanh (x-i c_1) \]