題目 5. (10 points) From the equation ex2+y2sin(2x)=4y,e^{x^2}+y^2\sin(2x)=4y,ex2+y2sin(2x)=4y, Solve dydx\dfrac{dy}{dx}dxdy in terms of xxx and yyy 解答 解法一 隱式微分後整理得 dydx=xexp(x2)+ysin(2x)+y2cos(2x)2.\boxed{\frac{\mathrm{d}y}{\mathrm{d}x} =\frac{x\exp(x^2)+y\sin(2x)+y^2\cos(2x)}2}.dxdy=2xexp(x2)+ysin(2x)+y2cos(2x).
