Internal problem ID [13757]
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: 22.12 (g).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=6 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=6*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} +3 x \right ) {\mathrm e}^{x}+c_{1} \cos \left (x \right )+c_{3} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 27
DSolve[y'''[x]-y''[x]+y'[x]-y[x]==6*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (3 x-3+c_3)+c_1 \cos (x)+c_2 \sin (x) \]