56.4.58 problem 55

Internal problem ID [8947]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 55
Date solved : Monday, January 27, 2025 at 05:20:37 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*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 20

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);
 

\[ y = \frac {x^{{3}/{2}} c_{2} +c_{1}}{x}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

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

AsymptoticDSolveValue[2*x^2*D[y[x],{x,2}]+3*x*D[y[x],x]-y[x]==0,y[x],{x,0,"6"-1}]
 

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