2.314   ODE No. 314

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

✓ Mathematica : cpu = 0.116592 (sec), leaf count = 188

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

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

✓ Maple : cpu = 0.113 (sec), leaf count = 158

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

\[y \left (x \right ) = \frac {{\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_{1} \right )}^{{1}/{4}}}{x}\]