Internal problem ID [5399]
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: 33.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y={\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve(diff(y(x),x$3)+diff(y(x),x$2)+diff(y(x),x)+y(x)=exp(x)+exp(-x)+sin(x),y(x), singsol=all)
\[ y = -\frac {x \cos \left (x \right )}{4}+\left (-\frac {x}{4}+\frac {1}{4}\right ) \sin \left (x \right )+\frac {x \,{\mathrm e}^{-x}}{2}+\frac {{\mathrm e}^{x}}{4}+\frac {{\mathrm e}^{-x}}{2}+\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} +c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.265 (sec). Leaf size: 55
DSolve[y'''[x]+y''[x]+y'[x]+y[x]==Exp[x]+Exp[-x]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} \left (2 e^{-x} \left (2 x+e^{2 x}+2+4 c_3\right )+(-2 x-1+8 c_1) \cos (x)+(-2 x+3+8 c_2) \sin (x)\right ) \]