2.132   ODE No. 132

\[ 3 x y'(x)-y(x)-3 x y(x)^4 \log (x)=0 \]

✓ Mathematica : cpu = 0.0918118 (sec), leaf count = 115

DSolve[-y[x] - 3*x*Log[x]*y[x]^4 + 3*x*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {(-2)^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}}\right \},\left \{y(x)\to \frac {2^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} 2^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}}\right \}\right \}\]

✓ Maple : cpu = 0.1 (sec), leaf count = 153

dsolve(3*x*diff(y(x),x)-3*x*ln(x)*y(x)^4-y(x) = 0,y(x))
 

\[y \left (x \right ) = \frac {{\left (-4 x \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1} \right )^{2}\right )}^{{1}/{3}}}{6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1}}\]