75.17.8 problem 558

Internal problem ID [17057]
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 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
Problem number : 558
Date solved : Tuesday, January 28, 2025 at 09:47:58 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-4*diff(y(x),x)=2*cos(4*x)^2,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{4 x} c_{1}}{4}-\frac {\sin \left (8 x \right )}{160}-\frac {\cos \left (8 x \right )}{80}-\frac {x}{4}+c_{2} \]

✓ Solution by Mathematica

Time used: 5.345 (sec). Leaf size: 47

DSolve[D[y[x],{x,2}]-4*D[y[x],x]==2*Cos[4*x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{4 K[2]} \left (c_1+\int _1^{K[2]}e^{-4 K[1]} (\cos (8 K[1])+1)dK[1]\right )dK[2]+c_2 \]