ODE
\[ 2 x \left (5 x^2+y(x)^2\right ) y'(x)=x^2 y(x)-y(x)^3 \] ODE Classification
[[_homogeneous, `class A`], _rational, _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.375279 (sec), leaf count = 216
\[\left \{\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\& ,5\right ]\right \}\right \}\]
Maple ✓
cpu = 0.336 (sec), leaf count = 29
\[\left [y \left (x \right ) = \RootOf \left (x^{9} \textit {\_C1} \,\textit {\_Z}^{45}-\textit {\_Z}^{18}-6 \textit {\_Z}^{9}-9\right )^{\frac {9}{2}} x\right ]\] Mathematica raw input
DSolve[2*x*(5*x^2 + y[x]^2)*y'[x] == x^2*y[x] - y[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> Root[3*E^(3*C[1])*Sqrt[x] + (E^(3*C[1])*#1^2)/x^(3/2) - #1^5 & , 1]}, {y[x] -> Root[3*E^(3*C[1])*Sqrt[x] + (E^(3*C[1])*#1^2)/x^(3/2) - #1^5 & , 2]}, {y[x] -> Root[3*E^(3*C[1])*Sqrt[x] + (E^(3*C[1])*#1^2)/x^(3/2) - #1^5 & , 3]}, {y[x] -> Root[3*E^(3*C[1])*Sqrt[x] + (E^(3*C[1])*#1^2)/x^(3/2) - #1^5 & , 4]}, {y[x] -> Root[3*E^(3*C[1])*Sqrt[x] + (E^(3*C[1])*#1^2)/x^(3/2) - #1^5 & , 5]}}
Maple raw input
dsolve(2*x*(5*x^2+y(x)^2)*diff(y(x),x) = x^2*y(x)-y(x)^3, y(x))
Maple raw output
[y(x) = RootOf(_C1*_Z^45*x^9-_Z^18-6*_Z^9-9)^(9/2)*x]