56.4.58 problem 55

Internal problem ID [8947]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 55
Date solved : Sunday, March 30, 2025 at 01:56:07 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 20

Order:=6; 
ode:=2*x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \frac {x^{{3}/{2}} c_2 +c_1}{x}+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

ode=2*x^2*D[y[x],{x,2}]+3*x*D[y[x],x]-y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \sqrt {x}+\frac {c_2}{x} \]

✓ Sympy. Time used: 0.746 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{2} \sqrt {x} + \frac {C_{1}}{x} + O\left (x^{6}\right ) \]