Internal problem ID [13723]
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 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=\left (72 x^{2}-1\right ) {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=(72*x^2-1)*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-6 x^{2}-x -1\right ) {\mathrm e}^{-2 x} {\mathrm e}^{4 x}+\left (c_{2} {\mathrm e}^{7 x}+c_{1} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 37
DSolve[y''[x]-3*y'[x]-10*y[x]==(72*x^2-1)*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{2 x} \left (6 x^2+x+1\right )+c_1 e^{-2 x}+c_2 e^{5 x} \]