ODE
\[ 8 y''(x)+9 y'(x)^4=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.2506 (sec), leaf count = 90
\[\left \{\left \{y(x)\to c_2-\frac {1}{3} \sqrt [3]{-\frac {1}{3}} (9 x-8 c_1){}^{2/3}\right \},\left \{y(x)\to \frac {(9 x-8 c_1){}^{2/3}}{3 \sqrt [3]{3}}+c_2\right \},\left \{y(x)\to \frac {1}{9} \left ((-3)^{2/3} (9 x-8 c_1){}^{2/3}+9 c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.347 (sec), leaf count = 51
\[\left [y \left (x \right ) = \left (x +\textit {\_C1} \right )^{\frac {2}{3}}+\textit {\_C2}, y \left (x \right ) = -\frac {\left (x +\textit {\_C1} \right )^{\frac {2}{3}} \left (1+i \sqrt {3}\right )}{2}+\textit {\_C2}, y \left (x \right ) = \frac {\left (x +\textit {\_C1} \right )^{\frac {2}{3}} \left (-1+i \sqrt {3}\right )}{2}+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[9*y'[x]^4 + 8*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/3*((-1/3)^(1/3)*(9*x - 8*C[1])^(2/3)) + 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))
Maple raw output
[y(x) = (x+_C1)^(2/3)+_C2, y(x) = -1/2*(x+_C1)^(2/3)*(1+I*3^(1/2))+_C2, y(x) = 1/2*(x+_C1)^(2/3)*(-1+I*3^(1/2))+_C2]