9.2.27 problem problem 57

Internal problem ID [961]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 57
Date solved : Monday, January 27, 2025 at 03:22:38 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

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

\[ y = c_1 +c_2 \,x^{3+\sqrt {3}}+c_3 \,x^{3-\sqrt {3}} \]

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 54

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

\[ y(x)\to \frac {c_2 x^{3+\sqrt {3}}}{3+\sqrt {3}}+\frac {c_1 x^{3-\sqrt {3}}}{3-\sqrt {3}}+c_3 \]