Internal problem ID [15318]
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: 548.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y={\mathrm e}^{x} \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=exp(x)*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (-8 c_{3} x^{2}-8 c_{2} x +\sin \left (2 x \right )-8 c_{1} -2 x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 33
DSolve[y'''[x]-3*y''[x]+3*y'[x]-y[x]==Exp[x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} e^x (-\sin (2 x)+8 (x (c_3 x+c_2)+c_1)) \]