Internal problem ID [11781]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+5 y=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+5*y(x)=2*exp(x)+10*exp(5*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{10 x}+{\mathrm e}^{6 x}+6 c_{1} {\mathrm e}^{4 x}+6 c_{2} \right ) {\mathrm e}^{-5 x}}{6} \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 36
DSolve[y''[x]+6*y'[x]+5*y[x]==2*Exp[x]+10*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^x \left (e^{4 x}+1\right )+c_1 e^{-5 x}+c_2 e^{-x} \]