Internal problem ID [13762]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.13 (e).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=3 \cos \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=3*x*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-3 x^{2}+8 c_{3} +3 x +9\right ) \sin \left (x \right )}{8}+\frac {\left (-3 x^{2}+8 c_{1} -9 x \right ) \cos \left (x \right )}{8}+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 52
DSolve[y'''[x]-y''[x]+y'[x]-y[x]==3*x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} \left (-\left (6 x^2+18 x+3-16 c_1\right ) \cos (x)+\left (-6 x^2+6 x+15+16 c_2\right ) \sin (x)+16 c_3 e^x\right ) \]