Internal problem ID [11771]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients.
Exercises page 135
Problem number: 41.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -8, y^{\prime \prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([diff(y(x),x$3)-3*diff(y(x),x$2)+4*y(x)=0,y(0) = 1, D(y)(0) = -8, (D@@2)(y)(0) = -4],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (6 x -23\right ) {\mathrm e}^{2 x}}{9}+\frac {32 \,{\mathrm e}^{-x}}{9} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 27
DSolve[{y'''[x]-3*y''[x]+4*y[x]==0,{y[0]==1,y'[0]==-8,y''[0]==-4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{9} e^{-x} \left (e^{3 x} (6 x-23)+32\right ) \]