Internal problem ID [5396]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 30.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 73
dsolve(diff(y(x),x$3)+y(x)=cos(x),y(x), singsol=all)
\[ y = -\frac {\cos \left (x \right )}{2 \left (2+\sqrt {3}\right ) \left (\sqrt {3}-2\right )}+\frac {\sin \left (x \right )}{2 \left (2+\sqrt {3}\right ) \left (\sqrt {3}-2\right )}+c_{1} {\mathrm e}^{-x}+c_{2} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) {\mathrm e}^{\frac {x}{2}}+c_{3} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) {\mathrm e}^{\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.515 (sec). Leaf size: 68
DSolve[y'''[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sin (x)}{2}+\frac {\cos (x)}{2}+c_1 e^{-x}+c_3 e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]