2.319   ODE No. 319

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

\[ \left (7 x y(x)^3+y(x)-5 x\right ) y'(x)+y(x)^4-5 y(x)=0 \] Mathematica : cpu = 0.177194 (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 = 0.033 (sec), leaf count = 35

\[\left \{x +\frac {2 y \left (x \right )^{5}-25 y \left (x \right )^{2}-10 c_{1}}{10 \left (y \left (x \right )^{3}-5\right )^{2} y \left (x \right )} = 0\right \}\]