Internal problem ID [14770]
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 (a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 y^{\prime } x +125 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x^3*diff(y(x),x$3)+16*x^2*diff(y(x),x$2)+79*x*diff(y(x),x)+125*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} \sin \left (3 \ln \left (x \right )\right ) x +c_{3} \cos \left (3 \ln \left (x \right )\right ) x +c_{1}}{x^{5}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[x^3*y'''[x]+16*x^2*y''[x]+79*x*y'[x]+125*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 x \cos (3 \log (x))+c_1 x \sin (3 \log (x))+c_3}{x^5} \]