\[ \left (4 x^3+2 x y(x)\right ) y'(x)+112 x^2 y(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 0.416322 (sec), leaf count = 1453
DSolve[112*x^2*y[x] + y[x]^2 + (4*x^3 + 2*x*y[x])*Derivative[1][y][x] == 0,y[x],x]
\[\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 = 1.314 (sec), leaf count = 31
dsolve((2*x*y(x)+4*x^3)*diff(y(x),x)+y(x)^2+112*x^2*y(x) = 0,y(x))
\[y \left (x \right ) = \frac {c_{1}}{x^{28} \RootOf \left (x^{30} \textit {\_Z}^{360}-24 x^{30} \textit {\_Z}^{330}-c_{1}\right )^{330}}\]