Internal problem ID [13713]
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 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=54 \,{\mathrm e}^{3 x} x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+9*y(x)=54*x^2*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+3 \left (x -\frac {1}{3}\right )^{2} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 36
DSolve[y''[x]+9*y[x]==54*x^2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{3 x} (1-3 x)^2+c_1 \cos (3 x)+c_2 \sin (3 x) \]