2.132   ODE No. 132

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ 3 x y'(x)-y(x)-3 x y(x)^4 \log (x)=0 \] Mathematica : cpu = 0.128854 (sec), leaf count = 115

\[\left \{\left \{y(x)\to \frac {(-2)^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}}\right \},\left \{y(x)\to \frac {2^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} 2^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}}\right \}\right \}\] Maple : cpu = 0.042 (sec), leaf count = 153

\[\left \{y \left (x \right ) = \frac {\left (-4 \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1}\right )^{2} x \right )^{\frac {1}{3}}}{6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1}}, y \left (x \right ) = \frac {\left (-4 \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1}\right )^{2} x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{12 x^{2} \ln \left (x \right )-6 x^{2}-8 c_{1}}, y \left (x \right ) = -\frac {\left (-4 \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1}\right )^{2} x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{12 x^{2} \ln \left (x \right )-6 x^{2}-8 c_{1}}\right \}\]