3.319   ODE No. 319

\[ \boxed { \left ( 7\,x \left ( y \left ( x \right ) \right ) ^{3}+y \left ( x \right ) -5\,x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{4}-5\,y \left ( x \right ) =0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.023503 (sec), leaf count = 302 \[ \left \{\left \{y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\& ,7\right ]\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 33 \[ \left \{ x-{\frac {1}{y \left ( x \right ) \left ( \left ( y \left ( x \right ) \right ) ^{3}-5 \right ) ^{2}} \left ( -{\frac { \left ( y \left ( x \right ) \right ) ^{5}}{5}}+{\frac {5\, \left ( y \left ( x \right ) \right ) ^{2}}{2}}+{\it \_C1} \right ) }=0 \right \} \]