Internal problem ID [1491]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient.
Page 483
Problem number: section 9.2, problem 27.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+19 y^{\prime \prime }+32 y^{\prime }+12 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = 3, y^{\prime }\relax (0) = -3, y^{\prime \prime }\relax (0) = -{\frac {7}{2}}, y^{\prime \prime \prime }\relax (0) = {\frac {31}{4}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve([4*diff(y(x),x$4)+8*diff(y(x),x$3)+19*diff(y(x),x$2)+32*diff(y(x),x)+12*y(x)=0,y(0) = 3, D(y)(0) = -3, (D@@2)(y)(0) = -7/2, (D@@3)(y)(0) = 31/4],y(x), singsol=all)
\[ y \relax (x ) = 2 \,{\mathrm e}^{-\frac {x}{2}}-\sin \left (2 x \right )+\cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 29
DSolve[{y''''[x]+2*y'''[x]-2*y''[x]-8*y'[x]-8*y[x]==0,{y[0]==5,y'[0]==-2,y''[0]==6,y'''[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (e^{4 x}+e^x (\sin (x)+3 \cos (x))+1\right ) \\ \end{align*}