#### 2.775   ODE No. 775

$y'(x)=\frac {-y(x)+\sqrt {y(x)}+x}{-y(x)+\sqrt {y(x)}+x+1}$ Mathematica : cpu = 0.157292 (sec), leaf count = 943

$\left \{\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {\#1}^6+(-6 x-6) \text {\#1}^5+\left (15 x^2+24 x+9\right ) \text {\#1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {\#1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {\#1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {\#1}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {\#1}^6+(-6 x-6) \text {\#1}^5+\left (15 x^2+24 x+9\right ) \text {\#1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {\#1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {\#1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {\#1}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {\#1}^6+(-6 x-6) \text {\#1}^5+\left (15 x^2+24 x+9\right ) \text {\#1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {\#1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {\#1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {\#1}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {\#1}^6+(-6 x-6) \text {\#1}^5+\left (15 x^2+24 x+9\right ) \text {\#1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {\#1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {\#1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {\#1}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {\#1}^6+(-6 x-6) \text {\#1}^5+\left (15 x^2+24 x+9\right ) \text {\#1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {\#1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {\#1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {\#1}\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [x^6-2 e^{3 c_1} x^3+e^{6 c_1}+\text {\#1}^6+(-6 x-6) \text {\#1}^5+\left (15 x^2+24 x+9\right ) \text {\#1}^4+\left (-20 x^3-36 x^2-18 x+2 e^{3 c_1}-4\right ) \text {\#1}^3+\left (15 x^4+24 x^3+9 x^2-6 e^{3 c_1} x-6 e^{3 c_1}\right ) \text {\#1}^2+\left (-6 x^5-6 x^4+6 e^{3 c_1} x^2+6 e^{3 c_1} x\right ) \text {\#1}\& ,6\right ]\right \}\right \}$ Maple : cpu = 0.059 (sec), leaf count = 44

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