Internal problem ID [15298]
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: 528.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }-2 y=8 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+4*diff(y(x),x)-2*y(x)=8*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\left (-2+\sqrt {6}\right ) x} c_{2} +{\mathrm e}^{-\left (2+\sqrt {6}\right ) x} c_{1} -\frac {16 \cos \left (2 x \right )}{25}-\frac {12 \sin \left (2 x \right )}{25} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 52
DSolve[y''[x]+4*y'[x]-2*y[x]==8*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-\left (\left (2+\sqrt {6}\right ) x\right )}+c_2 e^{\left (\sqrt {6}-2\right ) x}-\frac {4}{25} (3 \sin (2 x)+4 \cos (2 x)) \]