#### 2.319   ODE No. 319

$\left (7 x y(x)^3+y(x)-5 x\right ) y'(x)+y(x)^4-5 y(x)=0$ Mathematica : cpu = 0.148077 (sec), leaf count = 302

$\left \{\left \{y(x)\to \text {Root}\left [10 \text {\#1}^7 x-100 \text {\#1}^4 x+2 \text {\#1}^5-25 \text {\#1}^2+250 \text {\#1} x-10 c_1\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {\#1}^7 x-100 \text {\#1}^4 x+2 \text {\#1}^5-25 \text {\#1}^2+250 \text {\#1} x-10 c_1\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {\#1}^7 x-100 \text {\#1}^4 x+2 \text {\#1}^5-25 \text {\#1}^2+250 \text {\#1} x-10 c_1\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {\#1}^7 x-100 \text {\#1}^4 x+2 \text {\#1}^5-25 \text {\#1}^2+250 \text {\#1} x-10 c_1\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {\#1}^7 x-100 \text {\#1}^4 x+2 \text {\#1}^5-25 \text {\#1}^2+250 \text {\#1} x-10 c_1\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {\#1}^7 x-100 \text {\#1}^4 x+2 \text {\#1}^5-25 \text {\#1}^2+250 \text {\#1} x-10 c_1\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [10 \text {\#1}^7 x-100 \text {\#1}^4 x+2 \text {\#1}^5-25 \text {\#1}^2+250 \text {\#1} x-10 c_1\& ,7\right ]\right \}\right \}$ Maple : cpu = 0.025 (sec), leaf count = 35

$\left \{ x+{\frac {2\, \left ( y \left ( x \right ) \right ) ^{5}-25\, \left ( y \left ( x \right ) \right ) ^{2}-10\,{\it \_C1}}{10\, \left ( \left ( y \left ( x \right ) \right ) ^{3}-5 \right ) ^{2}y \left ( x \right ) }}=0 \right \}$