5.13 problem Exercise 11.14, page 97

Internal problem ID [3999]

Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number: Exercise 11.14, page 97.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+y \cos \relax (x )-{\mathrm e}^{2 x}=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

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

\[ y \relax (x ) = \left (\int {\mathrm e}^{2 x +\sin \relax (x )}d x +c_{1}\right ) {\mathrm e}^{-\sin \relax (x )} \]

Solution by Mathematica

Time used: 0.609 (sec). Leaf size: 32

DSolve[y'[x]+y[x]*Cos[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-\sin (x)} \left (\int _1^xe^{2 K[1]+\sin (K[1])}dK[1]+c_1\right ) \\ \end{align*}