Equation linear in x: solve dx/dy + Px = Q

1. A.
   $\left(\frac{1}{4},\frac{1}{2}\right)$
2. B.
   $\left(\frac{1}{4},-\frac{1}{2}\right)$
3. C.
   $\left(\frac{1}{3},-\frac{1}{3}\right)$
4. D.
   $\left(-\frac{1}{3},\frac{1}{3}\right)$

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1. A.
   1
2. B.
   2
3. C.
   3
4. D.
   4

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1. A.
   $2xe^{\tan^{- 1}y} = e^{2\tan^{- 1}y} + k$, where k is the constant of integration
2. B.
   $x \cdot e^{\tan^{- 1}y} = e^{\tan^{- 1}y} + k$, where k is the constant of integration
3. C.
   $x \cdot e^{2\tan^{- 1}y} = e^{\tan^{- 1}y} + k$, where k is the constant of integration
4. D.
   $\ x = 2 + k \cdot e^{- \tan^{- 1}y}$, where k is the constant of integration

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1. A.
   $x + y + 1 = c$, where $c$ is a constant of integration
2. B.
   $x + y + 1 = ce^y$, where $c$ is a constant of integration
3. C.
   $x + y + 1 = ce^{-y}$, where $c$ is a constant of integration
4. D.
   $x + y - 1 = ce^{-y}$, where $c$ is a constant of integration

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1. A.
   $e^{\tan^{-1}t}$
2. B.
   $-e^{\tan^{-1}t}$
3. C.
   $e^{-\tan^{-1}t}$
4. D.
   $-e^{-\tan^{-1}t}$

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1. A.
   $x = (c + y^2)y$, where c is the constant of integration
2. B.
   $y = (c + y^2)x$, where c is the constant of integration
3. C.
   $x = (c + y)y$, where c is the constant of integration
4. D.
   $y = (c + x^2)$, where c is the constant of integration

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1. A.
   $x = e^{-\frac{y}{x}}$
2. B.
   $y = e^{-\frac{y}{x}} + 1$
3. C.
   $x = e^{\frac{x}{y}} - 1$
4. D.
   $y = e^{\frac{x}{y}}$

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1. A.
   $e^{\sin y} = x + c$
2. B.
   $xe^{\sin y} = \dfrac{e^{2\sin y}}{2} + c$
3. C.
   $2x\cos y = e^x + c$
4. D.
   $\sin y - e^{\sin y} = c$

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