Internal problem ID [312]
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 58.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 26
dsolve(x^3*diff(y(x),x$3)+6*x^2*diff(y(x),x$2)+7*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+\frac {c_{2} \ln \relax (x )}{x}+\frac {c_{3} \ln \relax (x )^{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 23
DSolve[x^3*y'''[x]+6*x^2*y''[x]+7*x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (x) (c_3 \log (x)+c_2)+c_1}{x} \\ \end{align*}