Internal problem ID [4282]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{-x} y^{2}-y+{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 16
dsolve(diff(y(x),x)= exp(-x)*y(x)^2+y(x)-exp(x),y(x), singsol=all)
\[ y \relax (x ) = i \tan \left (i x +c_{1}\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.276 (sec). Leaf size: 19
DSolve[y'[x]== Exp[-x]*y[x]^2+y[x]-Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^x \tanh (x-i c_1) \\ \end{align*}