Internal problem ID [11784]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 10.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y=8 x \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=8*x*exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 c_{2} \cos \left (x \right )+2 c_{3} \sin \left (x \right )-4 x -1\right ) {\mathrm e}^{-2 x}}{2}+{\mathrm e}^{2 x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 40
DSolve[y'''[x]+2*y''[x]-3*y'[x]-10*y[x]==8*x*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-2 x} \left (-4 x+2 c_3 e^{4 x}+2 c_2 \cos (x)+2 c_1 \sin (x)-1\right ) \]