Find the integrating factor and solve the following equations:
( 𝑦 − 𝑥^2) 𝑑𝑥 +( 𝑥^2sin 𝑦 − 𝑥 )𝑑𝑦 = 0
Try 1x2\frac{1}{x^2}x21 as an integrating factor:
(yx2−1)dx+(siny−1x)dy=0d(−yx−x−cosy)=0yx+x+cosy=Const\left( \frac{y}{x^2}-1 \right) dx+\left( \sin y-\frac{1}{x} \right) dy=0\\d\left( -\frac{y}{x}-x-\cos y \right) =0\\\frac{y}{x}+x+\cos y=Const(x2y−1)dx+(siny−x1)dy=0d(−xy−x−cosy)=0xy+x+cosy=Const
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