ODE
\[ -45 y''(x) y'''(x) y''''(x)+9 y''(x)^2 y'''''(x)+40 \left (y'''(x)\right )^3=0 \] ODE Classification
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.308706 (sec), leaf count = 43
\[\left \{\left \{y(x)\to c_5 x-\frac {4 \sqrt {x (c_3 x+c_2)+c_1}}{c_2{}^2-4 c_1 c_3}+c_4\right \}\right \}\]
Maple ✓
cpu = 2.706 (sec), leaf count = 105
\[\left [y \left (x \right ) = \int \int \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\RootOf \left (-\ln \left (\textit {\_f} \right )-6 \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_k}}{\sqrt {\textit {\_k}^{4}-\textit {\_C1}}}d \textit {\_k} \right )+\textit {\_C2} \right ) \textit {\_f}^{\frac {3}{2}}}d \textit {\_f} \right )+x +\textit {\_C3} \right )d x d x +\textit {\_C4} x +\textit {\_C5}, y \left (x \right ) = \int \int \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\RootOf \left (-\ln \left (\textit {\_f} \right )+6 \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_k}}{\sqrt {\textit {\_k}^{4}-\textit {\_C1}}}d \textit {\_k} \right )+\textit {\_C2} \right ) \textit {\_f}^{\frac {3}{2}}}d \textit {\_f} \right )+x +\textit {\_C3} \right )d x d x +\textit {\_C4} x +\textit {\_C5}\right ]\] Mathematica raw input
DSolve[40*y'''[x]^3 - 45*y''[x]*y'''[x]*y''''[x] + 9*y''[x]^2*y'''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-4*Sqrt[C[1] + x*(C[2] + x*C[3])])/(C[2]^2 - 4*C[1]*C[3]) + C[4] + x*C[5]}}
Maple raw input
dsolve(9*diff(diff(y(x),x),x)^2*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-45*diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x)+40*diff(diff(diff(y(x),x),x),x)^3 = 0, y(x))
Maple raw output
[y(x) = Int(Int(RootOf(-Intat(1/RootOf(-ln(_f)-6*Intat(1/(_k^4-_C1)^(1/2)*_k,_k = _Z)+_C2)/_f^(3/2),_f = _Z)+x+_C3),x),x)+_C4*x+_C5, y(x) = Int(Int(RootOf(-Intat(1/RootOf(-ln(_f)+6*Intat(1/(_k^4-_C1)^(1/2)*_k,_k = _Z)+_C2)/_f^(3/2),_f = _Z)+x+_C3),x),x)+_C4*x+_C5]