Internal problem ID [311]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \relax (x ) = c_{1}+c_{2} x^{3+\sqrt {3}}+c_{3} x^{3-\sqrt {3}} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 52
DSolve[x^3*y'''[x]-3*x^2*y''[x]+x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^{3+\sqrt {3}}+\left (2+\sqrt {3}\right ) c_1 x^{3-\sqrt {3}}}{3+\sqrt {3}}+c_3 \\ \end{align*}