Internal problem ID [13396]
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: 22.7 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=\left (12 x -4\right ) {\mathrm e}^{-5 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=(12*x-4)*exp(-5*x),y(x), singsol=all)
\[ y = {\mathrm e}^{x} c_{2} +x \,{\mathrm e}^{x} c_{1} +\frac {{\mathrm e}^{-5 x} x}{3} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 27
DSolve[y''[x]-2*y'[x]+y[x]==(12*x-4)*Exp[-5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-5 x} x+e^x (c_2 x+c_1) \]