Internal problem ID [14771]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 64 (b).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 y^{\prime } x +48 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(x^4*diff(y(x),x$4)+5*x^3*diff(y(x),x$3)-12*x^2*diff(y(x),x$2)-12*x*diff(y(x),x)+48*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} x^{7}+c_{3} x^{5}+c_{4} x +c_{1}}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[x^4*y''''[x]+5*x^3*y'''[x]-12*x^2*y''[x]-12*x*y'[x]+48*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_4 x^7+c_3 x^5+c_2 x+c_1}{x^3} \]