Internal problem ID [11776]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-8 y=4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=4*exp(2*x)-21*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 c_{2} {\mathrm e}^{7 x}-{\mathrm e}^{5 x}+2 c_{1} {\mathrm e}^{x}-6\right ) {\mathrm e}^{-3 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 38
DSolve[y''[x]-2*y'[x]-8*y[x]==4*Exp[2*x]-21*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{2} e^{-3 x} \left (e^{5 x}+6\right )+c_1 e^{-2 x}+c_2 e^{4 x} \]