Internal problem ID [15348]
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: 579.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=4 x +\sin \left (x \right )+\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=4*x+sin(x)+sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = 1+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{2 x}+x +\frac {4 \cos \left (x \right )}{25}+\frac {3 \sin \left (x \right )}{25}+\frac {\cos \left (2 x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.324 (sec). Leaf size: 45
DSolve[y''[x]-4*y'[x]+4*y[x]==4*x+Sin[x]+Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+\frac {3 \sin (x)}{25}+\frac {4 \cos (x)}{25}+\frac {1}{8} \cos (2 x)+c_2 e^{2 x} x+c_1 e^{2 x}+1 \]