Internal problem ID [309]
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 55.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x^3*diff(y(x),x$3)-x^2*diff(y(x),x$2)+x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +x^{2} c_{2} +c_{3} x^{2} \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 35
DSolve[x^3*y'''[x]-x^2*y''[x]+x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} (2 c_1-c_2) x^2+\frac {1}{2} c_2 x^2 \log (x)+c_3 \\ \end{align*}