#### 2.314   ODE No. 314

$x y(x)^3 y'(x)+y(x)^4-x \sin (x)=0$ Mathematica : cpu = 0.146554 (sec), leaf count = 188

$\left \{\left \{y(x)\to -\frac {\sqrt [4]{c_1-4 x^4 \cos (x)+16 x^3 \sin (x)+48 x^2 \cos (x)-96 x \sin (x)-96 \cos (x)}}{x}\right \},\left \{y(x)\to -\frac {i \sqrt [4]{c_1-4 x^4 \cos (x)+16 x^3 \sin (x)+48 x^2 \cos (x)-96 x \sin (x)-96 \cos (x)}}{x}\right \},\left \{y(x)\to \frac {i \sqrt [4]{c_1-4 x^4 \cos (x)+16 x^3 \sin (x)+48 x^2 \cos (x)-96 x \sin (x)-96 \cos (x)}}{x}\right \},\left \{y(x)\to \frac {\sqrt [4]{c_1-4 x^4 \cos (x)+16 x^3 \sin (x)+48 x^2 \cos (x)-96 x \sin (x)-96 \cos (x)}}{x}\right \}\right \}$ Maple : cpu = 0.036 (sec), leaf count = 158

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