Internal problem ID [229]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=2 x^{2} {\mathrm e}^{3 x}+5} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+9*y(x)=2*x^2*exp(3*x)+5,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} +\frac {5}{9}+\frac {\left (x -\frac {1}{3}\right )^{2} {\mathrm e}^{3 x}}{9} \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 50
DSolve[y''[x]+9*y[x]==2*x^2*Exp[3*x]+5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{81} \left (9 e^{3 x} x^2-6 e^{3 x} x+e^{3 x}+81 c_1 \cos (3 x)+81 c_2 \sin (3 x)+45\right ) \]