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]]
\[ \boxed {16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y=96 x^{\frac {5}{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
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)
\[ y \left (x \right ) = \frac {4 c_{4} x^{3}+x^{4}+4 c_{3} x^{2}+4 c_{2} x +4 c_{1}}{4 x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.008 (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]
\[ y(x)\to \frac {x^4+4 c_4 x^3+4 c_3 x^2+4 c_2 x+4 c_1}{4 x^{3/2}} \]