Internal problem ID [14773]
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 (d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 y^{\prime } x +45 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(x^4*diff(y(x),x$4)+8*x^3*diff(y(x),x$3)+27*x^2*diff(y(x),x$2)+35*x*diff(y(x),x)+45*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \sin \left (2 \ln \left (x \right )\right )}{x}+\frac {c_{2} \cos \left (2 \ln \left (x \right )\right )}{x}+c_{3} \sin \left (3 \ln \left (x \right )\right )+c_{4} \cos \left (3 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 44
DSolve[x^4*y''''[x]+8*x^3*y'''[x]+27*x^2*y''[x]+35*x*y'[x]+45*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \cos (2 \log (x))+c_3 x \cos (3 \log (x))+c_1 \sin (2 \log (x))+c_4 x \sin (3 \log (x))}{x} \]