2.314   ODE No. 314

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

\[ \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3 \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^4-\text {Global$\grave { }$x} \sin (\text {Global$\grave { }$x})=0 \] Mathematica : cpu = 0.0436798 (sec), leaf count = 188

\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to -\frac {\sqrt [4]{c_1-4 \text {Global$\grave { }$x}^4 \cos (\text {Global$\grave { }$x})+16 \text {Global$\grave { }$x}^3 \sin (\text {Global$\grave { }$x})+48 \text {Global$\grave { }$x}^2 \cos (\text {Global$\grave { }$x})-96 \text {Global$\grave { }$x} \sin (\text {Global$\grave { }$x})-96 \cos (\text {Global$\grave { }$x})}}{\text {Global$\grave { }$x}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to -\frac {i \sqrt [4]{c_1-4 \text {Global$\grave { }$x}^4 \cos (\text {Global$\grave { }$x})+16 \text {Global$\grave { }$x}^3 \sin (\text {Global$\grave { }$x})+48 \text {Global$\grave { }$x}^2 \cos (\text {Global$\grave { }$x})-96 \text {Global$\grave { }$x} \sin (\text {Global$\grave { }$x})-96 \cos (\text {Global$\grave { }$x})}}{\text {Global$\grave { }$x}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {i \sqrt [4]{c_1-4 \text {Global$\grave { }$x}^4 \cos (\text {Global$\grave { }$x})+16 \text {Global$\grave { }$x}^3 \sin (\text {Global$\grave { }$x})+48 \text {Global$\grave { }$x}^2 \cos (\text {Global$\grave { }$x})-96 \text {Global$\grave { }$x} \sin (\text {Global$\grave { }$x})-96 \cos (\text {Global$\grave { }$x})}}{\text {Global$\grave { }$x}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\sqrt [4]{c_1-4 \text {Global$\grave { }$x}^4 \cos (\text {Global$\grave { }$x})+16 \text {Global$\grave { }$x}^3 \sin (\text {Global$\grave { }$x})+48 \text {Global$\grave { }$x}^2 \cos (\text {Global$\grave { }$x})-96 \text {Global$\grave { }$x} \sin (\text {Global$\grave { }$x})-96 \cos (\text {Global$\grave { }$x})}}{\text {Global$\grave { }$x}}\right \}\right \}\]

Maple : cpu = 0.051 (sec), leaf count = 170

\[ \left \{ y \left ( x \right ) ={\frac {1}{x}\sqrt [4]{-4\,{x}^{4}\cos \left ( x \right ) +16\,\sin \left ( x \right ) {x}^{3}+48\,{x}^{2}\cos \left ( x \right ) -96\,\cos \left ( x \right ) -96\,x\sin \left ( x \right ) +{\it \_C1}}},y \left ( x \right ) ={\frac {-i}{x}\sqrt [4]{-4\,{x}^{4}\cos \left ( x \right ) +16\,\sin \left ( x \right ) {x}^{3}+48\,{x}^{2}\cos \left ( x \right ) -96\,\cos \left ( x \right ) -96\,x\sin \left ( x \right ) +{\it \_C1}}},y \left ( x \right ) ={\frac {i}{x}\sqrt [4]{-4\,{x}^{4}\cos \left ( x \right ) +16\,\sin \left ( x \right ) {x}^{3}+48\,{x}^{2}\cos \left ( x \right ) -96\,\cos \left ( x \right ) -96\,x\sin \left ( x \right ) +{\it \_C1}}},y \left ( x \right ) =-{\frac {1}{x}\sqrt [4]{-4\,{x}^{4}\cos \left ( x \right ) +16\,\sin \left ( x \right ) {x}^{3}+48\,{x}^{2}\cos \left ( x \right ) -96\,\cos \left ( x \right ) -96\,x\sin \left ( x \right ) +{\it \_C1}}} \right \} \]