Internal problem ID [14725]
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: 16.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x^3*diff(y(x),x$3)+4*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}+c_{2} \sin \left (2 \ln \left (x \right )\right )+c_{3} \cos \left (2 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[x^3*y'''[x]+4*x^2*y''[x]+6*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_3}{x}+c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x)) \]