ODE
\[ 2 y(x) y''(x)=a+y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.164408 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {x^2 \left (a+c_1{}^2\right )}{4 c_2}+c_1 x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.189 (sec), leaf count = 22
\[\left [y \left (x \right ) = \frac {x^{2} \left (\textit {\_C1}^{2}+a \right )}{4 \textit {\_C2}}+\textit {\_C1} x +\textit {\_C2}\right ]\] Mathematica raw input
DSolve[2*y[x]*y''[x] == a + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + (x^2*(a + C[1]^2))/(4*C[2]) + C[2]}}
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = a+diff(y(x),x)^2, y(x))
Maple raw output
[y(x) = 1/4*x^2*(_C1^2+a)/_C2+_C1*x+_C2]