Internal problem ID [6526]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 55.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 27
Order:=6; dsolve(2*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)-y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {x^{\frac {3}{2}} c_{2}+c_{1}}{x}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 18
AsymptoticDSolveValue[2*x^2*y''[x]+3*x*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x}+\frac {c_2}{x} \]