75.20.21 problem 660

Internal problem ID [17155]
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 : Tuesday, January 28, 2025 at 09:54:39 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 5.320 (sec). Leaf size: 45

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

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