ODE
\[ x^2 y''(x)=\left (3 x-2 y'(x)\right ) y'(x) \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.275615 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \frac {1}{2} \left (x^2-c_1 \log \left (x^2+c_1\right )+2 c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.466 (sec), leaf count = 22
\[\left [y \left (x \right ) = \frac {x^{2}}{2}+\frac {\textit {\_C1} \ln \left (x^{2}-\textit {\_C1} \right )}{2}+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[x^2*y''[x] == (3*x - 2*y'[x])*y'[x],y[x],x]
Mathematica raw output
{{y[x] -> (x^2 + 2*C[2] - C[1]*Log[x^2 + C[1]])/2}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x) = (3*x-2*diff(y(x),x))*diff(y(x),x), y(x))
Maple raw output
[y(x) = 1/2*x^2+1/2*_C1*ln(x^2-_C1)+_C2]