Internal problem ID [1575]
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 14.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y-96 x^{\frac {5}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(16*x^4*diff(y(x),x$4)+96*x^3*diff(y(x),x$3)+72*x^2*diff(y(x),x$2)-24*x*diff(y(x),x)+9*y(x)=96*x^(5/2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{\frac {5}{2}}}{4}+\frac {c_{1}}{x^{\frac {3}{2}}}+\frac {c_{2}}{\sqrt {x}}+c_{3} \sqrt {x}+c_{4} x^{\frac {3}{2}} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 41
DSolve[16*x^4*y''''[x]+96*x^3*y'''[x]+72*x^2*y''[x]-24*x*y'[x]+9*y[x]==96*x^(5/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^4+4 c_4 x^3+4 c_3 x^2+4 c_2 x+4 c_1}{4 x^{3/2}} \\ \end{align*}