Internal problem ID [14103]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 81.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1, y^{\prime \prime }\left (0\right ) = -1, y^{\prime \prime \prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 41
dsolve([diff(y(x),x$4)+25/2*diff(y(x),x$2)-5*diff(y(x),x)+629/16*y(x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = -1, (D@@3)(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (74 \cos \left (3 x \right )+20 \sin \left (3 x \right )\right ) {\mathrm e}^{-\frac {x}{2}}}{208}-\frac {37 \left (\cos \left (2 x \right )-\frac {3 \sin \left (2 x \right )}{2}\right ) {\mathrm e}^{\frac {x}{2}}}{104} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 47
DSolve[{y''''[x]+25/2*y''[x]-5*y'[x]+629/16*y[x]==0,{y[0]==0,y'[0]==1,y''[0]==-1,y'''[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{208} e^{-x/2} \left (111 e^x \sin (2 x)+20 \sin (3 x)-74 e^x \cos (2 x)+74 \cos (3 x)\right ) \]