Internal problem ID [14756]
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: 50.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x^3*diff(y(x),x$3)+3*x^2*diff(y(x),x$2)-3*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} x^{2}+\frac {c_{3}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 26
DSolve[x^3*y'''[x]+3*x^2*y''[x]-3*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 x^2}{2}-\frac {c_1}{2 x^2}+c_3 \]