Internal problem ID [12474]
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: 10.
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: 0.063 (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)
\[ y \left (x \right ) = -\frac {7 \cosh \left (3 x \right )}{9}+\frac {10 \sinh \left (3 x \right )}{27}-\frac {x}{9}-\frac {2}{9} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 33
DSolve[{y''[x]-9*y[x]==x+2,{y[0]==-1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{54} e^{-3 x} \left (-6 e^{3 x} (x+2)-11 e^{6 x}-31\right ) \]