Internal problem ID [12438]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+9 y=27 x +18} \] With initial conditions \begin {align*} [y \left (0\right ) = 23, y^{\prime }\left (0\right ) = 21] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)+9*y(x)=27*x+18,y(0) = 23, D(y)(0) = 21],y(x), singsol=all)
\[ y \left (x \right ) = 2+21 \cos \left (3 x \right )+6 \sin \left (3 x \right )+3 x \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 22
DSolve[{y''[x]+9*y[x]==27*x+18,{y[0]==23,y'[0]==21}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x+6 \sin (3 x)+21 \cos (3 x)+2 \]