12.20.4 problem section 9.4, problem 14

Internal problem ID [2225]
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
Date solved : Monday, January 27, 2025 at 05:43:47 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} 16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y&=96 x^{{5}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.011 (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)
 

\[ y = \frac {4 c_4 \,x^{3}+x^{4}+4 c_3 \,x^{2}+4 c_2 x +4 c_1}{4 x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 41

DSolve[16*x^4*D[y[x],{x,4}]+96*x^3*D[y[x],{x,3}]+72*x^2*D[y[x],{x,2}]-24*x*D[y[x],x]+9*y[x]==96*x^(5/2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4+4 c_4 x^3+4 c_3 x^2+4 c_2 x+4 c_1}{4 x^{3/2}} \]