Internal problem ID [12475]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+9 y=x +2} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)+9*y(x)=x+2,y(0) = -1, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {11 \cos \left (3 x \right )}{9}+\frac {8 \sin \left (3 x \right )}{27}+\frac {x}{9}+\frac {2}{9} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 26
DSolve[{y''[x]+9*y[x]==x+2,{y[0]==-1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{27} (3 x+8 \sin (3 x)-33 \cos (3 x)+6) \]