Internal problem ID [13444]
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 (g).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=5 x^{5} {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=5*x^5*exp(2*x),y(x), singsol=all)
\[ y = \frac {\left (625 x^{5}-5625 x^{4}+28000 x^{3}-91200 x^{2}+187320 x -188376\right ) {\mathrm e}^{2 x}}{625}+c_{1} \cos \left (x \right )+c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 58
DSolve[y'''[x]-y''[x]+y'[x]-y[x]==5*x^5*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (e^x \left (x^5-9 x^4+\frac {224 x^3}{5}-\frac {3648 x^2}{25}+\frac {37464 x}{125}-\frac {188376}{625}\right )+c_3\right )+c_1 \cos (x)+c_2 \sin (x) \]