4.30.21 \(x^2 y''(x)-3 x y'(x)+4 y(x)=0\)

ODE
\[ x^2 y''(x)-3 x y'(x)+4 y(x)=0 \] ODE Classification

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Book solution method
TO DO

Mathematica
cpu = 0.00729568 (sec), leaf count = 18

\[\left \{\left \{y(x)\to x^2 \left (2 c_2 \log (x)+c_1\right )\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 14

\[ \left \{ y \left ( x \right ) ={x}^{2} \left ( \ln \left ( x \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \] Mathematica raw input

DSolve[4*y[x] - 3*x*y'[x] + x^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x^2*(C[1] + 2*C[2]*Log[x])}}

Maple raw input

dsolve(x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x^2*(ln(x)*_C2+_C1)