74.15.47 problem 50

Internal problem ID [16486]
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
Date solved : Tuesday, January 28, 2025 at 09:09:18 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = c_{1} +c_{2} x^{2}+\frac {c_{3}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 26

DSolve[x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^2}{2}-\frac {c_1}{2 x^2}+c_3 \]