2.1844   ODE No. 1844

\[ 4 y(x)^2 y^{(3)}(x)+15 y'(x)^3-18 y(x) y'(x) y''(x)=0 \]

✓ Mathematica : cpu = 0.183019 (sec), leaf count = 20

DSolve[15*Derivative[1][y][x]^3 - 18*y[x]*Derivative[1][y][x]*Derivative[2][y][x] + 4*y[x]^2*Derivative[3][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {1}{\left (c_3 x^2+c_2 x+c_1\right ){}^2}\right \}\right \}\]

✓ Maple : cpu = 0.401 (sec), leaf count = 75

dsolve(4*y(x)^2*diff(diff(diff(y(x),x),x),x)-18*y(x)*diff(y(x),x)*diff(diff(y(x),x),x)+15*diff(y(x),x)^3=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{\int \operatorname {RootOf}\left (-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_h}^{2}+\sqrt {\textit {\_h}^{2} c_{1} +c_{1}^{2}}+c_{1}}d \textit {\_h} \right )+x +c_{2} \right )d x +c_{3}}\]