26.5.13 problem Exercise 11.14, page 97

Internal problem ID [6986]
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
Date solved : Tuesday, September 30, 2025 at 04:07:44 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \cos \left (x \right )&={\mathrm e}^{2 x} \end{align*}

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

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

\[ y = \left (\int {\mathrm e}^{2 x +\sin \left (x \right )}d x +c_1 \right ) {\mathrm e}^{-\sin \left (x \right )} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 52

ode=D[y[x],x]+y[x]*Cos[x]==Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 4.532 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*cos(x) - exp(2*x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \int \left (y{\left (x \right )} \cos {\left (x \right )} - e^{2 x}\right ) e^{\sin {\left (x \right )}}\, dx = C_{1} \]