Internal problem ID [15316]
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: 546.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$3)-y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {x \sqrt {3}}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {x \sqrt {3}}{2}\right )+c_{1} {\mathrm e}^{x}-\frac {\sin \left (x \right )}{2}+\frac {\cos \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.419 (sec). Leaf size: 66
DSolve[y'''[x]-y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sin (x)}{2}+\frac {\cos (x)}{2}+c_1 e^x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_3 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]