Internal problem ID [13404]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.10 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=4 x \,{\mathrm e}^{6 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=4*x*exp(6*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{-2 x}+c_{1} {\mathrm e}^{5 x}+\frac {\left (8 x -9\right ) {\mathrm e}^{6 x}}{16} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 36
DSolve[y''[x]-3*y'[x]-10*y[x]==4*x*Exp[6*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} e^{6 x} (8 x-9)+c_1 e^{-2 x}+c_2 e^{5 x} \]