미분방정식 $\left (y^ {2} +x y^ {3} \right) d x+ \left (5 y^ {2} -x y+y^ {3} \sin y \right) d y=0$ 의 해는?

• ①$\displaystyle x y^ {2} + \frac{x^ {2} y^ {3}} {2} +x y^ {3} \sin y=C$
• ②$\displaystyle \frac{y^ {3}} {3} + \frac{x y^ {4}} {4} +5 y^ {2} x- \frac{x^ {2} y} {2} +x y^ {3} \sin y=C$
• ③$\displaystyle \frac{x} {y^ {2}} +y^ {3} x-x \cos y=C$
• ④$\displaystyle \frac{x} {y} + \frac{x^ {2}} {2} +5 \ln y- \cos y=C$