ODE
\[ 2 y(x) y''(x)=3 y'(x)^2+4 y(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0932977 (sec), leaf count = 17
\[\left \{\left \{y(x)\to c_2 \sec ^2\left (2 c_1+x\right )\right \}\right \}\]
Maple ✓
cpu = 0.042 (sec), leaf count = 19
\[ \left \{ -{\it \_C1}\,\sin \left ( x \right ) +{\it \_C2}\,\cos \left ( x \right ) +2\,{\frac {1}{\sqrt {y \left ( x \right ) }}}=0 \right \} \] Mathematica raw input
DSolve[2*y[x]*y''[x] == 4*y[x]^2 + 3*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> C[2]*Sec[x + 2*C[1]]^2}}
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = 3*diff(y(x),x)^2+4*y(x)^2, y(x),'implicit')
Maple raw output
-_C1*sin(x)+_C2*cos(x)+2/y(x)^(1/2) = 0