Internal problem ID [12482]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+9 y=18 \,{\mathrm e}^{3 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)+9*y(x)=18*exp(3*x),y(0) = -1, D(y)(0) = 6],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x}-2 \cos \left (3 x \right )+\sin \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 21
DSolve[{y''[x]+9*y[x]==18*Exp[3*x],{y[0]==-1,y'[0]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x}+\sin (3 x)-2 \cos (3 x) \]