75.20.21 problem 660

Internal problem ID [17076]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 660
Date solved : Thursday, March 13, 2025 at 09:13:10 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 5.32 (sec). Leaf size: 45

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

\[ y(x)\to \int _1^xe^{-K[2]} \left (c_1+\int _1^{K[2]}e^{3 K[1]} \cos \left (e^{K[1]}\right )dK[1]\right )dK[2]+c_2 \]

✓ Sympy. Time used: 1.082 (sec). Leaf size: 20

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

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