Internal problem ID [15327]
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 ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Superposition principle. Exercises page 137
Problem number: 558.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }=2 \cos \left (4 x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-4*diff(y(x),x)=2*cos(4*x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{4 x}}{4}-\frac {\sin \left (8 x \right )}{160}-\frac {\cos \left (8 x \right )}{80}-\frac {x}{4}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.243 (sec). Leaf size: 40
DSolve[y''[x]-4*y'[x]==2*Cos[4*x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x}{4}-\frac {1}{160} \sin (8 x)-\frac {1}{80} \cos (8 x)+\frac {1}{4} c_1 e^{4 x}+c_2 \]