20.13 problem section 9.4, problem 33

Internal problem ID [1584]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
Problem number: section 9.4, problem 33.
ODE order: 4.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _exact, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y-40 x^{3}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = -1, y^{\prime }\left (-1\right ) = -7, y^{\prime \prime }\left (-1\right ) = -1, y^{\prime \prime \prime }\left (-1\right ) = -31] \end {align*}

Solution by Maple

Time used: 0.047 (sec). Leaf size: 30

dsolve([x^4*diff(y(x),x$4)+5*x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)-6*x*diff(y(x),x)+6*y(x)=40*x^3,y(-1) = -1, D(y)(-1) = -7, (D@@2)(y)(-1) = -1, (D@@3)(y)(-1) = -31],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x^{5} \ln \relax (x )-1+\left (-i \pi -2\right ) x^{5}+x^{3}+x}{x^{2}} \]

Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 32

DSolve[{x^4*y''''[x]+5*x^3*y'''[x]-3*x^2*y''[x]-6*x*y'[x]+6*y[x]==40*x^3,{y[-1]==-1,y'[-1]==-7,y''[-1]==-1,y'''[-1]==-31}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {(-2-i \pi ) x^5+x^5 \log (x)+x^3+x-1}{x^2} \\ \end{align*}