Internal problem ID [13761]
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 (d).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=30 x \cos \left (2 x \right )} \]
✓ 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)=30*x*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (30 x -98\right ) \cos \left (2 x \right )}{15}+\frac {\left (-60 x -64\right ) \sin \left (2 x \right )}{15}+c_{1} \cos \left (x \right )+c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 49
DSolve[y'''[x]-y''[x]+y'[x]-y[x]==30*x*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -4 x \sin (2 x)-\frac {64}{15} \sin (2 x)+\left (2 x-\frac {98}{15}\right ) \cos (2 x)+c_3 e^x+c_1 \cos (x)+c_2 \sin (x) \]