ODE
\[ 8 y''(x)+9 y'(x)^4=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0323541 (sec), leaf count = 90
\[\left \{\left \{y(x)\to c_2-\frac {1}{3} \sqrt [3]{-\frac {1}{3}} \left (9 x-8 c_1\right ){}^{2/3}\right \},\left \{y(x)\to \frac {\left (9 x-8 c_1\right ){}^{2/3}}{3 \sqrt [3]{3}}+c_2\right \},\left \{y(x)\to \frac {1}{9} \left ((-3)^{2/3} \left (9 x-8 c_1\right ){}^{2/3}+9 c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.239 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C1}+x \right ) ^{{\frac {2}{3}}}+{\it \_C2},y \left ( x \right ) ={\frac {i\sqrt {3}-1}{2} \left ( {\it \_C1}+x \right ) ^{{\frac {2}{3}}}}+{\it \_C2},y \left ( x \right ) =-{\frac {i\sqrt {3}+1}{2} \left ( {\it \_C1}+x \right ) ^{{\frac {2}{3}}}}+{\it \_C2} \right \} \] Mathematica raw input
DSolve[9*y'[x]^4 + 8*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((-1/3)^(1/3)*(9*x - 8*C[1])^(2/3))/3 + C[2]}, {y[x] -> (9*x - 8*C[1])^(2/3)/(3*3^(1/3)) + C[2]}, {y[x] -> ((-3)^(2/3)*(9*x - 8*C[1])^(2/3) + 9*C[2])/9}}
Maple raw input
dsolve(8*diff(diff(y(x),x),x)+9*diff(y(x),x)^4 = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1+x)^(2/3)+_C2, y(x) = -1/2*(_C1+x)^(2/3)*(I*3^(1/2)+1)+_C2, y(x) = 1/2*(_C1+x)^(2/3)*(I*3^(1/2)-1)+_C2