Internal problem ID [15256]
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: 486.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+8 y={\mathrm e}^{2 x} \left (-\cos \left (2 x \right )+\sin \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
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)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{2 x} \left (\left (x -4 c_{1} +\frac {1}{2}\right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (x -4 c_{2} \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 41
DSolve[y''[x]-4*y'[x]+8*y[x]==Exp[2*x]*(Sin[2*x]-Cos[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{8} e^{2 x} ((2 x+1-8 c_2) \cos (2 x)+2 (x-4 c_1) \sin (2 x)) \]