大学文科数学微积分 本人很渣，对数学题很慢热，需要详细十分精细的解题过程！！！求详细解答过程

Question

大学文科数学微积分 本人很渣，对数学题很慢热，需要详细十分精细的解题过程！！！求详细解答过程，拜托了

Answer 1

y=cx^2
dy/dx=2cx
dy=2cxdx
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y'=2xy^2
dy/dx=2xy^2
dy/(y^2)=2xdx
i.e. -1/y=x^2+C where C is a constant
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y'=ycosx
dy/dx=ycosx
dy/y=cosxdx
ln|y|=sinx+C
i.e. y=Be^(sinx) where B is a constant
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(1+x^2)dy+2xydx=0
dy+(x^2dy+2xydx)=0
dy+[x^2dy+yd(x^2)]=0
dy+d(y*x^2)=0
dy=-d(y*x^2)
y=-y*x^2+C where C is a constant
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xydx+(1-x^2)^(1/2)dy=0
(1-x^2)^(1/2)dy=-xydx
dy/y=-xdx/[(1-x^2)^(1/2)]
dy/y=[(1-x^2)^(-1/2)]*[d(1-x^2)]/2
ln|y|=[(1-x^2)^(1/2)]/4+C where C is a constant