2.293   ODE No. 293

$x \left (y(x)^2-3 x\right ) y'(x)+2 y(x)^3-5 x y(x)=0$ Mathematica : cpu = 0.169175 (sec), leaf count = 661

$\left \{\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,7\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,8\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,9\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,10\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,11\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,12\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,13\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,14\right ]\right \},\left \{y(x)\to \text {Root}\left [-\frac {25 \text {\#1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}-\text {\#1}^{15}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\& ,15\right ]\right \}\right \}$ Maple : cpu = 0.27 (sec), leaf count = 35

$\left \{ \ln \left ( x \right ) -{\it \_C1}-{\frac {2}{65}\ln \left ( {\frac {5\, \left ( y \left ( x \right ) \right ) ^{2}-13\,x}{x}} \right ) }+{\frac {6}{13}\ln \left ( {y \left ( x \right ) {\frac {1}{\sqrt {x}}}} \right ) }=0 \right \}$