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 = 0.320734 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \frac {2304 c_1^2}{\left (3 c_1^2 x^2+6 c_2 c_1^2 x+3 c_2^2 c_1^2+128\right ){}^2}\right \}\right \}\]
Maple ✓
cpu = 0.305 (sec), leaf count = 147
\[ \left \{ -12\,{\frac {y \left ( x \right ) \left ( 8\,\sqrt {y \left ( x \right ) }-{\it \_C1} \right ) \sqrt {8\,y \left ( x \right ) -{\it \_C1}\,\sqrt {y \left ( x \right ) }}}{\sqrt {-24\, \left ( y \left ( x \right ) \right ) ^{3}+3\,{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{5/2}}{\it \_C1}\,\sqrt {\sqrt {y \left ( x \right ) } \left ( 8\,\sqrt {y \left ( x \right ) }-{\it \_C1} \right ) }}}-x-{\it \_C2}=0,12\,{\frac {y \left ( x \right ) \left ( 8\,\sqrt {y \left ( x \right ) }-{\it \_C1} \right ) \sqrt {8\,y \left ( x \right ) -{\it \_C1}\,\sqrt {y \left ( x \right ) }}}{\sqrt {-24\, \left ( y \left ( x \right ) \right ) ^{3}+3\,{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{5/2}}{\it \_C1}\,\sqrt {\sqrt {y \left ( x \right ) } \left ( 8\,\sqrt {y \left ( x \right ) }-{\it \_C1} \right ) }}}-x-{\it \_C2}=0 \right \} \] 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),'implicit')
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)-_C1*y(x)^(1/2))^(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)-_C1*y(x)^(1/2))^(1/2)/_C1/(y(x)^(1/2)*(8*y(x)^(1/2)-_C1))^(1/2)-x-_C2 = 0