Internal problem ID [11725]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 16, Higher order linear equations with constant coefficients. Exercises page
153
Problem number: 16.1 (ii).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+2*y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-15 \sin \left (x \right )-3 \cos \left (x \right )}{6 \left (5+2 \sqrt {3}\right ) \left (-5+2 \sqrt {3}\right )}+{\mathrm e}^{x} c_{1} +{\mathrm e}^{\left (1+\sqrt {3}\right ) x} c_{2} +{\mathrm e}^{-\left (\sqrt {3}-1\right ) x} c_{3} \]
✓ Solution by Mathematica
Time used: 0.206 (sec). Leaf size: 49
DSolve[y'''[x]-3*y''[x]+2*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{26} \left (5 \sin (x)+\cos (x)+26 e^x \left (c_1 e^{-\sqrt {3} x}+c_2 e^{\sqrt {3} x}+c_3\right )\right ) \]