Internal problem ID [10848]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 47.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{3} y^{\prime \prime }-y^{\prime } x +y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve([x^3*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,x],y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{-\frac {1}{x}} c_{1} +c_{2} \right ) x \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 20
DSolve[x^3*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (c_2 e^{-1/x}+c_1\right ) \\ \end{align*}