ODE
\[ 4 y(x) y''(x)=3 y'(x)^2-4 y(x) \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0998619 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \frac {\left (c_1^2 x^2+2 c_2 c_1^2 x+c_2^2 c_1^2-64\right ){}^2}{256 c_1^2}\right \}\right \}\]
Maple ✓
cpu = 0.151 (sec), leaf count = 67
\[ \left \{ -4\,{\frac {\sqrt {{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{3/2}+4\,y \left ( x \right ) }}{\sqrt {y \left ( x \right ) }{\it \_C1}}}-x-{\it \_C2}=0,4\,{\frac {\sqrt {{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{3/2}+4\,y \left ( x \right ) }}{\sqrt {y \left ( x \right ) }{\it \_C1}}}-x-{\it \_C2}=0,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[4*y[x]*y''[x] == -4*y[x] + 3*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-64 + x^2*C[1]^2 + 2*x*C[1]^2*C[2] + C[1]^2*C[2]^2)^2/(256*C[1]^2)}}
Maple raw input
dsolve(4*y(x)*diff(diff(y(x),x),x) = 3*diff(y(x),x)^2-4*y(x), y(x),'implicit')
Maple raw output
y(x) = 0, -4*(_C1*y(x)^(3/2)+4*y(x))^(1/2)/y(x)^(1/2)/_C1-x-_C2 = 0, 4*(_C1*y(x)^(3/2)+4*y(x))^(1/2)/y(x)^(1/2)/_C1-x-_C2 = 0