Question 1

Find a general solution for the differential equation: $\frac{dy}{dx}+y=1$

Accepted Answer

$y=1+Ce^{-x}$

Answer

$y=x-Ce^{-x}$

Answer

$y=1-Ce^{-x}$

Answer

$y=x+Ce^{x}$

Question 2

Find a general solution for the differential equation: $y^{'}=x-y$

Accepted Answer

$y=x-1+Ce^{-x}$

Answer

$y=x-1-Ce^{-x}$

Answer

$y=x+1-Ce^{x}$

Answer

$y=x+1+Ce^{x}$

Question 3

Find a general solution for the differential equation: $xy^{'}+y=\sqrt{x}$

Accepted Answer

$y=\frac{2}{3}\sqrt{x}+\frac{C}{x}$

Answer

$y=\frac{1}{3}\sqrt{x}-\frac{C}{x}$

Answer

$y=\frac{5}{3}\sqrt{x}+\frac{C}{x}$

Answer

$y=\frac{4}{3}\sqrt{x}+\frac{C}{x}$

Question 4

Find a general solution to the differential equation $xy^{'}-2y=x^{2}$ (x>0)

Accepted Answer

$y=x^{2}(\ln{x}+C)$

Answer

$y=x^{3}(\ln{2x^{2}}+C)$

Answer

$y=x^{3}(\ln{x^{2}}+C)$

Answer

$y=x^{2}(\ln{2x}+C)$

Question 5

Find a general solution to the differential equation $y^{''}-y^{'}-6y=0$

Accepted Answer

$C_{1}e^{3x}+c_{2}e^{-2x}$

Answer

$C_{1}e^{4x}+c_{2}e^{x}$

Answer

$C_{1}e^{x}-c_{2}e^{2x}$

Answer

$C_{1}e^{x}-c_{2}e^{-x}$

Question 6

Find a general solution to the differential equation $y^{''}+2y=0$

Accepted Answer

$C_{1}\cos({\sqrt{2}x)}+C_{2}\sin{(\sqrt{2}x)}$

Answer

$C_{1}\cos({-\sqrt{2}x)}+C_{2}\sin{(-\sqrt{2}x)}$

Answer

$C_{1}\cos({\sqrt{2}x)}-C_{2}\sin{(-\sqrt{2}x)}$

Answer

$C_{1}\cos({\sqrt{2}x)}-C_{2}\sin{(\sqrt{2}x)}$

Question 7

Find a general solution to the differential equation $4y^{''}+4y^{'}+y=0$

Accepted Answer

$C_{1}e^{-\frac{x}{2}}+xC_{2}e^{-\frac{x}{2}}$

Answer

$C_{1}e^{-\frac{x}{2}}+C_{2}e^{-\frac{x}{2}}$

Answer

$C_{1}e^{\frac{x}{2}}+xC_{2}e^{\frac{x}{2}}$

Answer

$C_{1}e^{\frac{x}{2}}+C_{2}e^{\frac{x}{2}}$

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