20.6.15 problem Problem 37

Internal problem ID [3710]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 37
Date solved : Monday, January 27, 2025 at 07:55:44 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(x^3*diff(y(x),x$3)+3*x^2*diff(y(x),x$2)-6*x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} +c_{2} x^{\sqrt {7}}+c_3 \,x^{-\sqrt {7}} \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 41

DSolve[x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]-6*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {c_1 x^{-\sqrt {7}}}{\sqrt {7}}+\frac {c_2 x^{\sqrt {7}}}{\sqrt {7}}+c_3 \]