ODE
\[ 12 y(x) y''(x)=15 y'(x)^2-8 y(x)^3 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.726376 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \frac {2304 c_1{}^2}{\left (3 c_1{}^2 x^2+6 c_2 c_1{}^2 x+128+3 c_2{}^2 c_1{}^2\right ){}^2}\right \}\right \}\]
Maple ✓
cpu = 0.512 (sec), leaf count = 147
\[\left [-\frac {12 y \left (x \right ) \left (8 \sqrt {y \left (x \right )}-\textit {\_C1} \right ) \sqrt {8 y \left (x \right )-\sqrt {y \left (x \right )}\, \textit {\_C1}}}{\sqrt {-24 y \left (x \right )^{3}+3 \textit {\_C1} y \left (x \right )^{\frac {5}{2}}}\, \textit {\_C1} \sqrt {\sqrt {y \left (x \right )}\, \left (8 \sqrt {y \left (x \right )}-\textit {\_C1} \right )}}-x -\textit {\_C2} = 0, \frac {12 y \left (x \right ) \left (8 \sqrt {y \left (x \right )}-\textit {\_C1} \right ) \sqrt {8 y \left (x \right )-\sqrt {y \left (x \right )}\, \textit {\_C1}}}{\sqrt {-24 y \left (x \right )^{3}+3 \textit {\_C1} y \left (x \right )^{\frac {5}{2}}}\, \textit {\_C1} \sqrt {\sqrt {y \left (x \right )}\, \left (8 \sqrt {y \left (x \right )}-\textit {\_C1} \right )}}-x -\textit {\_C2} = 0\right ]\] Mathematica raw input
DSolve[12*y[x]*y''[x] == -8*y[x]^3 + 15*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (2304*C[1]^2)/(128 + 3*x^2*C[1]^2 + 6*x*C[1]^2*C[2] + 3*C[1]^2*C[2]^2)^2}}
Maple raw input
dsolve(12*y(x)*diff(diff(y(x),x),x) = 15*diff(y(x),x)^2-8*y(x)^3, y(x))
Maple raw output
[-12/(-24*y(x)^3+3*_C1*y(x)^(5/2))^(1/2)*y(x)*(8*y(x)^(1/2)-_C1)*(8*y(x)-y(x)^(1/2)*_C1)^(1/2)/_C1/(y(x)^(1/2)*(8*y(x)^(1/2)-_C1))^(1/2)-x-_C2 = 0, 12/(-24*y(x)^3+3*_C1*y(x)^(5/2))^(1/2)*y(x)*(8*y(x)^(1/2)-_C1)*(8*y(x)-y(x)^(1/2)*_C1)^(1/2)/_C1/(y(x)^(1/2)*(8*y(x)^(1/2)-_C1))^(1/2)-x-_C2 = 0]