Internal problem ID [11782]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+10 y=5 x \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+10*y(x)=5*x*exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (10 c_{1} \cos \left (3 x \right )+10 c_{2} \sin \left (3 x \right )\right ) {\mathrm e}^{-x}}{10}+\frac {\left (5 x +1\right ) {\mathrm e}^{-2 x}}{10} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 41
DSolve[y''[x]+2*y'[x]+10*y[x]==5*x*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{10} e^{-2 x} \left (5 x+10 c_2 e^x \cos (3 x)+10 c_1 e^x \sin (3 x)+1\right ) \]