#### 2.245   ODE No. 245

$\left (4 x^3+2 x y(x)\right ) y'(x)+112 x^2 y(x)+y(x)^2=0$ Mathematica : cpu = 0.411906 (sec), leaf count = 1453

$\left \{\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,7\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,8\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,9\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,10\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,11\right ]\right \},\left \{y(x)\to \text {Root}\left [-1521681143169024 \text {\#1} x^{22}-697437190619136 \text {\#1}^2 x^{20}-145299414712320 \text {\#1}^3 x^{18}-18162426839040 \text {\#1}^4 x^{16}-1513535569920 \text {\#1}^5 x^{14}-88289574912 \text {\#1}^6 x^{12}-3678732288 \text {\#1}^7 x^{10}-109486080 \text {\#1}^8 x^8-2280960 \text {\#1}^9 x^6-31680 \text {\#1}^{10} x^4-264 \text {\#1}^{11} x^2-\text {\#1}^{12}+\frac {e^{30 c_1}}{x^6}\& ,12\right ]\right \}\right \}$ Maple : cpu = 2.141 (sec), leaf count = 31

$\left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{{x}^{28} \left ( {\it RootOf} \left ( {x}^{30}{{\it \_Z}}^{360}-24\,{x}^{30}{{\it \_Z}}^{330}-{\it \_C1} \right ) \right ) ^{330}}} \right \}$