#### 2.713   ODE No. 713

$y'(x)=\frac {-a^2-a b y(x)-a b \sqrt {x}+a b+b^2 x+b^2}{a \left (a (-y(x))-a \sqrt {x}+a+b x+b\right )}$ Mathematica : cpu = 0.0907574 (sec), leaf count = 649

$\left \{\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [-\frac {24 \text {\#1}^4 x^2}{a^4}+\frac {8 \text {\#1}^3 x^{3/2}}{a^6}+\frac {9 \text {\#1}^2 x}{a^8}+\text {\#1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {6 \text {\#1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,1\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [-\frac {24 \text {\#1}^4 x^2}{a^4}+\frac {8 \text {\#1}^3 x^{3/2}}{a^6}+\frac {9 \text {\#1}^2 x}{a^8}+\text {\#1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {6 \text {\#1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,2\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [-\frac {24 \text {\#1}^4 x^2}{a^4}+\frac {8 \text {\#1}^3 x^{3/2}}{a^6}+\frac {9 \text {\#1}^2 x}{a^8}+\text {\#1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {6 \text {\#1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,3\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [-\frac {24 \text {\#1}^4 x^2}{a^4}+\frac {8 \text {\#1}^3 x^{3/2}}{a^6}+\frac {9 \text {\#1}^2 x}{a^8}+\text {\#1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {6 \text {\#1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,4\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [-\frac {24 \text {\#1}^4 x^2}{a^4}+\frac {8 \text {\#1}^3 x^{3/2}}{a^6}+\frac {9 \text {\#1}^2 x}{a^8}+\text {\#1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {6 \text {\#1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,5\right ]}\right \},\left \{y(x)\to -\frac {a \sqrt {x}-a-b x-b}{a}+\frac {1}{a^2 \text {Root}\left [-\frac {24 \text {\#1}^4 x^2}{a^4}+\frac {8 \text {\#1}^3 x^{3/2}}{a^6}+\frac {9 \text {\#1}^2 x}{a^8}+\text {\#1}^6 \left (16 x^3+16 e^{12 c_1}\right )-\frac {6 \text {\#1} \sqrt {x}}{a^{10}}+\frac {1}{a^{12}}\& ,6\right ]}\right \}\right \}$ Maple : cpu = 0.656 (sec), leaf count = 86

$\left \{ y \left ( x \right ) ={\frac {1}{2\,a} \left ( 3\,\tanh \left ( {\it RootOf} \left ( 729\,{x}^{3} \left ( \tanh \left ( {\it \_Z} \right ) \right ) ^{6}{a}^{6}-2187\,{x}^{3} \left ( \tanh \left ( {\it \_Z} \right ) \right ) ^{4}{a}^{6}+2187\,{x}^{3} \left ( \tanh \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{6}-729\,{a}^{6}{x}^{3}+64\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it \_C1} \right ) \right ) \sqrt {x}a-a\sqrt {x}+2\,a+ \left ( 2\,x+2 \right ) b \right ) } \right \}$