Internal problem ID [12803]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 5.203 (sec). Leaf size: 15
dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0,y(0) = 0, D(y)(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{-x}+{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 18
DSolve[{y''[x]-y'[x]-2*y[x]==0,{y[0]==0,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (e^{3 x}-1\right ) \]