Internal problem ID [14774]
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 (e).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(x^4*diff(y(x),x$4)+10*x^3*diff(y(x),x$3)+27*x^2*diff(y(x),x$2)+21*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (c_{4} \ln \left (x \right )+c_{2} \right ) \cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right ) \left (c_{3} \ln \left (x \right )+c_{1} \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 34
DSolve[x^4*y''''[x]+10*x^3*y'''[x]+27*x^2*y''[x]+21*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {(c_4 \log (x)+c_3) \cos (\log (x))+(c_2 \log (x)+c_1) \sin (\log (x))}{x} \]