Internal problem ID [1583]
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 32.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y-6 x=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = 2, y^{\prime }\relax (1) = 0, y^{\prime \prime }\relax (1) = 4, y^{\prime \prime \prime }\relax (1) = -{\frac {37}{4}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 27
dsolve([4*x^4*diff(y(x),x$4)+24*x^3*diff(y(x),x$3)+23*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=6*x,y(1) = 2, D(y)(1) = 0, (D@@2)(y)(1) = 4, (D@@3)(y)(1) = -37/4],y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \relax (x ) x^{\frac {5}{2}}-x^{2}+x^{\frac {5}{2}}+\sqrt {x}+x}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 26
DSolve[{4*x^4*y''''[x]+24*x^3*y'''[x]+23*x^2*y''[x]-x*y'[x]+y[x]==6*x,{y[1]==2,y'[1]==0,y''[1]==4,y'''[1]==-37/4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\sqrt {x}+\frac {1}{\sqrt {x}}+\frac {1}{x}+x \log (x) \\ \end{align*}