Internal problem ID [14726]
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: 17.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+2 y^{\prime } x -2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x^3*diff(y(x),x$3)+2*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{1} +c_{2} \sin \left (\ln \left (x \right )\right )+c_{3} \cos \left (\ln \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[x^3*y'''[x]+2*x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (c_2 \cos (\log (x))+c_1 \sin (\log (x))+c_3) \]