Internal problem ID [14673]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number: 63 (b).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2, y^{\prime \prime }\left (0\right ) = -1, y^{\prime \prime \prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 36
dsolve([diff(y(t),t$4)-8*diff(y(t),t$3)+30*diff(y(t),t$2)-56*diff(y(t),t)+49*y(t)=0,y(0) = 1, D(y)(0) = 2, (D@@2)(y)(0) = -1, (D@@3)(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\left (\left (\frac {21 t}{2}-3\right ) \cos \left (\sqrt {3}\, t \right )+\sqrt {3}\, \sin \left (\sqrt {3}\, t \right ) \left (t -\frac {7}{2}\right )\right ) {\mathrm e}^{2 t}}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 49
DSolve[{y''''[t]-8*y'''[t]+30*y''[t]-56*y'[t]+49*y[t]==0,{y[0]==1,y'[0]==2,y''[0]==-1,y'''[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {1}{6} e^{2 t} \left (\sqrt {3} (2 t-7) \sin \left (\sqrt {3} t\right )+3 (7 t-2) \cos \left (\sqrt {3} t\right )\right ) \]