Internal problem ID [13709]
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: 22.5 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=9 x^{4}-9} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+9*y(x)=9*x^4-9,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+x^{4}-\frac {4 x^{2}}{3}-\frac {19}{27} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 33
DSolve[y''[x]+9*y[x]==9*x^4-9,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^4-\frac {4 x^2}{3}+c_1 \cos (3 x)+c_2 \sin (3 x)-\frac {19}{27} \]