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### Re: [大學]工程數學的問題

lskuo 寫到:
Anonymous 寫到:1、 exsin y-2x+(excos y+1)y'=0

2、[x+y2 (y2 - x2)^(1/2)] (dy/dx)=y - xy( y2 - x2)^(1/2)

3、(dy/dx)=x3(y-x)^2 + y•x^(-1)

Hint:
1. By noticing that [ex sin(y)]' = ex [ sin(y) + y' cos(y) ], one can re-write the equation as the following
[ex sin(y)]' + y' = 2x
Next integrate the both sides.

3. Let z = y/x and solve z.
y' = z +xz' = x5(z-1)2 + z
Now the equation becomes separable.

1. [ex sin(y)]' + y' = 2這個我還沒學到怎積分

### Re: [大學]工程數學的問題

Anonymous 寫到:1、 exsin y-2x+(excos y+1)y'=0

2、[x+y2 (y2 - x2)^(1/2)] (dy/dx)=y - xy( y2 - x2)^(1/2)

3、(dy/dx)=x3(y-x)^2 + y•x^(-1)

Hint:
1. By noticing that [ex sin(y)]' = ex [ sin(y) + y' cos(y) ], one can re-write the equation as the following
[ex sin(y)]' + y' = 2x
Next integrate the both sides.

3. Let z = y/x and solve z.
y' = z +xz' = x5(z-1)2 + z
Now the equation becomes separable.

### [大學]工程數學的問題

1、 exsin y-2x+(excos y+1)y'=0

2、[x+y2 (y2 - x2)^(1/2)] (dy/dx)=y - xy( y2 - x2)^(1/2)

3、(dy/dx)=x3(y-x)^2 + y•x^(-1)