Internal problem ID [14727]
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: 18.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(x^3*diff(y(x),x$3)+3*x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{3}+c_{3} \ln \left (x \right )+c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 23
DSolve[x^3*y'''[x]+3*x^2*y''[x]-2*x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_3 x^3+c_2 \log (x)+c_1}{x} \]