Internal problem ID [13417]
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: 22.11 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=x^{3} {\mathrm e}^{-x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 61
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=x^3*exp(-x)*sin(x),y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +\frac {2 \,{\mathrm e}^{-x} \left (\left (x^{3}+\frac {31}{13} x^{2}+\frac {1220}{507} x +\frac {19100}{19773}\right ) \cos \left (x \right )+\frac {3 \left (x^{3}+\frac {18}{13} x^{2}+\frac {138}{169} x +\frac {360}{2197}\right ) \sin \left (x \right )}{2}\right )}{39} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 70
DSolve[y''[x]-4*y'[x]+5*y[x]==x^3*Exp[-x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x} \left (\left (39546 x^3+94302 x^2+95160 x+771147 c_2 e^{3 x}+38200\right ) \cos (x)+27 \left (2197 x^3+3042 x^2+1794 x+28561 c_1 e^{3 x}+360\right ) \sin (x)\right )}{771147} \]