dy/dx as a function of x + y (trig, exponential or ratio): substitute v = x + y

1. A.
   $y=x+\log(x+y)+c$
2. B.
   $y=x-\log(x+y)+c$
3. C.
   $y=x-\log(2x+y)+c$
4. D.
   $y=x^2+\log(x+y)+c$

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1. A.
   $y=\sin(x+y)+c$
2. B.
   $y=\tan(x+y)+c$
3. C.
   $y=\tan\frac{x+y}{2}+c$
4. D.
   $y=\frac{1}{2}\tan(x+y)+c$

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1. A.
   $\log\left[1 + \tan\left(\dfrac{x + y}{2}\right)\right] = y + c$, where c is the constant of integration
2. B.
   $\log\left[1 - \tan\left(\dfrac{x + y}{2}\right)\right] = y + c$, where c is the constant of integration
3. C.
   $\log\left[1 + \tan\left(\dfrac{x + y}{2}\right)\right] = x + c$, where c is the constant of integration
4. D.
   $\log\left[1 - \tan\left(\dfrac{x + y}{2}\right)\right] = x + c$, where c is the constant of integration

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1. A.
   $\cot\left(\dfrac{x + y}{2}\right) = x + c$
2. B.
   $\tan\left(\dfrac{x + y}{2}\right) = x + c$
3. C.
   $-\sin(x + y) = x + c$
4. D.
   $\sec(x - y) + x = c$

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1. A.
   $e^{x+y} = x + c$, where $c$ is integral constant
2. B.
   $(x + c)e^{x+y} - 1 = 0$, where $c$ is integral constant
3. C.
   $(x + c)e^{x+y} + 1 = 0$, where $c$ is integral constant
4. D.
   $e^{x+y} = x + y + c$, where $c$ is integral constant

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1. A.
   $(x + y + C)e^{x+y} = 0$
2. B.
   $(x + C)e^{x+y} = 0$
3. C.
   $(x - C)e^{x+y} = 0$
4. D.
   $(x + C)e^{x+y} + 1 = 0$

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