Internal problem ID [11816]
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: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y={\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+9*y(x)=exp(3*x)+exp(-3*x)+exp(3*x)*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+\frac {\left (2 \sin \left (3 x \right )-4 \cos \left (3 x \right )+5\right ) {\mathrm e}^{3 x}}{90}+\frac {{\mathrm e}^{-3 x}}{18} \]
✓ Solution by Mathematica
Time used: 0.997 (sec). Leaf size: 57
DSolve[y''[x]+9*y[x]==Exp[3*x]+Exp[-3*x]+Exp[3*x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{90} \left (5 e^{-3 x} \left (e^{6 x}+1\right )+\left (-4 e^{3 x}+90 c_1\right ) \cos (3 x)+2 \left (e^{3 x}+45 c_2\right ) \sin (3 x)\right ) \]