Internal problem ID [13763]
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 (f).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=3 x \,{\mathrm e}^{x} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=3*x*exp(x)*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-30 x +57\right ) \cos \left (x \right )+\left (15 x +24\right ) \sin \left (x \right )+25 c_{2} \right ) {\mathrm e}^{x}}{25}+c_{1} \cos \left (x \right )+c_{3} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 49
DSolve[y'''[x]-y''[x]+y'[x]-y[x]==3*x*Exp[x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^x+\left (e^x \left (\frac {57}{25}-\frac {6 x}{5}\right )+c_1\right ) \cos (x)+\left (\frac {3}{25} e^x (5 x+8)+c_2\right ) \sin (x) \]