Internal problem ID [14772]
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 (c).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 y^{\prime } x +15 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^4*diff(y(x),x$4)+14*x^3*diff(y(x),x$3)+55*x^2*diff(y(x),x$2)+65*x*diff(y(x),x)+15*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{3} \sin \left (\ln \left (x \right )\right ) x +c_{4} \cos \left (\ln \left (x \right )\right ) x +c_{2} x^{2}+c_{1}}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 32
DSolve[x^4*y''''[x]+14*x^3*y'''[x]+55*x^2*y''[x]+65*x*y'[x]+15*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_4 x^2+c_2 x \cos (\log (x))+c_1 x \sin (\log (x))+c_3}{x^3} \]