Internal problem ID [15344]
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: 575.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=1+8 \cos \left (x \right )+{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=1+8*cos(x)+exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} -\sin \left (x \right )+\cos \left (x \right )+\frac {1}{5}+{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.341 (sec). Leaf size: 40
DSolve[y''[x]-4*y'[x]+5*y[x]==1+8*Cos[x]+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x}+\left (1+c_2 e^{2 x}\right ) \cos (x)+\left (-1+c_1 e^{2 x}\right ) \sin (x)+\frac {1}{5} \]