Internal problem ID [15325]
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: 556.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime }={\mathrm e}^{2 x}+\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$3)+4*diff(y(x),x)=exp(2*x)+sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-8 c_{2} -1\right ) \cos \left (2 x \right )}{16}+\frac {\left (-x +4 c_{1} \right ) \sin \left (2 x \right )}{8}+c_{3} +\frac {{\mathrm e}^{2 x}}{16} \]
✓ Solution by Mathematica
Time used: 0.836 (sec). Leaf size: 44
DSolve[y'''[x]+4*y'[x]==Exp[2*x]+Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{32} \left (2 e^{2 x}-((3+16 c_2) \cos (2 x))-4 (x-4 c_1) \sin (2 x)\right )+c_3 \]