Internal problem ID [11819]
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: 45.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+13 y=x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 68
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+13*y(x)=x*exp(-3*x)*sin(2*x)+x^2*exp(-2*x)*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {3 \left (\left (\frac {13 x^{2}}{12}-\frac {26 c_{1}}{3}-\frac {39}{16}\right ) \cos \left (2 x \right )+{\mathrm e}^{x} \left (x^{2}-\frac {2}{13} x -\frac {180}{169}\right ) \cos \left (3 x \right )+\frac {2 \,{\mathrm e}^{x} \left (x^{2}-\frac {41}{13} x +\frac {563}{338}\right ) \sin \left (3 x \right )}{3}-\frac {13 \sin \left (2 x \right ) \left (x +16 c_{2} \right )}{24}\right ) {\mathrm e}^{-3 x}}{26} \]
✓ Solution by Mathematica
Time used: 1.921 (sec). Leaf size: 82
DSolve[y''[x]+6*y'[x]+13*y[x]==x*Exp[-3*x]*Sin[2*x]+x^2*Exp[-2*x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-3 x} \left (-32 e^x \left (338 x^2-1066 x+563\right ) \sin (3 x)-96 e^x \left (169 x^2-26 x-180\right ) \cos (3 x)-2197 \left (8 x^2-1-64 c_2\right ) \cos (2 x)+8788 (x+16 c_1) \sin (2 x)\right )}{140608} \]