Internal problem ID [278]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.2, Higher-Order Linear Differential Equations. General solutions of Linear
Equations. Page 288
Problem number: problem 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -9 y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x^{3} \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-9*y(x)=0,x^3],y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{3}+\frac {c_{2}}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[x^2*y''[x]+x*y'[x]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^6+c_1}{x^3} \\ \end{align*}