Internal problem ID [13710]
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: 22.6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=x^{3}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)+9*y(x)=x^3,y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \sin \left (3 x \right )}{81}+\frac {x^{3}}{9}-\frac {2 x}{27} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 24
DSolve[{y''[x]+9*y[x]==x^3,{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{81} \left (9 x^3-6 x+2 \sin (3 x)\right ) \]