Linear equation with a given condition: value of y at a point or the curve through a point

1. A.
   $-\frac{4}{9}\pi^2$
2. B.
   $\frac{4}{9\sqrt{3}}\pi^2$
3. C.
   $-\frac{8}{9\sqrt{3}}\pi^2$
4. D.
   $-\frac{8}{9}\pi^2$

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1. A.
   $\frac{7}{64}$
2. B.
   $\frac{1}{4}$
3. C.
   $\frac{1}{36}$
4. D.
   $\frac{49}{16}$

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

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

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1. A.
   $y + xe^x = 0$
2. B.
   $ye^x + x = 0$
3. C.
   $ye^x - x = 0$
4. D.
   $y - xe^x = 0$

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

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1. A.
   $y\left( 1 + x^{2} \right) = 4x^{3}$
2. B.
   $4\left( 1 + x^{2} \right) = 4 + y^{2}$
3. C.
   $3y\left( 1 + x^{2} \right) = 4x^{3}$
4. D.
   $1 + y^{2} = 4x^{3} + 1$

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

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