Internal problem ID [15255]
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. Trial and error method. Exercises page 132
Problem number: 485.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+8 y={\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+8*y(x)=exp(2*x)*(sin(2*x)+cos(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (16 c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{2 x}\right ) \sin \left (2 x \right )}{16}+{\mathrm e}^{-2 x} \cos \left (2 x \right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.287 (sec). Leaf size: 38
DSolve[y''[x]+4*y'[x]+8*y[x]==Exp[2*x]*(Sin[2*x]+Cos[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} e^{-2 x} \left (16 c_2 \cos (2 x)+\left (e^{4 x}+16 c_1\right ) \sin (2 x)\right ) \]