Internal problem ID [12461]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.5, page 221
Problem number: 1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 5, y^{\prime \prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(y(x),x$3)-3*diff(y(x),x$2)-4*diff(y(x),x)+12*y(x)=0,y(0) = 1, D(y)(0) = 5, (D@@2)(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \left (-{\mathrm e}^{5 x}+3 \,{\mathrm e}^{4 x}-1\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 26
DSolve[{y'''[x]-3*y''[x]-4*y'[x]+12*y[x]==0,{y[0]==1,y'[0]==5,y''[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{-2 x} \left (-3 e^{4 x}+e^{5 x}+1\right ) \]