Internal problem ID [1489]
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 25.
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 }-13 y^{\prime \prime }+9 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 3, y^{\prime \prime }\relax (0) = 1, y^{\prime \prime \prime }\relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve([4*diff(y(x),x$4)-13*diff(y(x),x$2)+9*y(x)=0,y(0) = 1, D(y)(0) = 3, (D@@2)(y)(0) = 1, (D@@3)(y)(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{-x}+2 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 12
DSolve[{4*y''''[x]-13*y''[x]+9*y[x]==0,{y[0]==1,y'[0]==3,y''[0]==1,y'''[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 \sinh (x)+\cosh (x) \\ \end{align*}