Internal problem ID [13443]
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]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=3 \cos \left (x \right ) x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
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)
\[ y = -\frac {3 \,{\mathrm e}^{x} \left (10 x -19\right ) \cos \left (x \right )}{25}+\frac {3 \,{\mathrm e}^{x} \left (5 x +8\right ) \sin \left (x \right )}{25}+c_{1} \cos \left (x \right )+c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right ) \]
✓ 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]
\[ y(x)\to c_3 e^x+\left (e^x \left (\frac {57}{25}-\frac {6 x}{5}\right )+c_1\right ) \cos (x)+\left (\frac {3}{25} e^x (5 x+8)+c_2\right ) \sin (x) \]