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13. Consider the linear DE $xy' = \frac{x^2 + xy}{x + y}$. Which value of a and b, the given DE will be homogenous? I. $a = 0$ and $b = 1$ II. $a = 1$ and $b = 0$ III. $a = 1$ and $b = 2$ IV. $a = 2$ and $b = 1$ 14. The roots of the characteristic equation of the third order homogenous DE is $r_1 = 0, r_2 = 1, r_3 = 1$. The general solution of the given DE is I. $y = c_1e^x + c_2e^x + c_3$ II. $y = c_1e^x + c_2xe^x + c_3$ III. $y = c_1e^x + c_2x^2e^x + c_3x$ IV. $y = c_1e^x + c_2e^x + c_3x$ V. 15. According to the drag equation the velocity of an object moving through a fluid can be modeled by the equation $y' = -ky$ where k is constant. An object moving through the water has an initial velocity of 40 m/s. One seconds later, the velocity has 30 m/s. What will the velocity in m/s be nineth seconds? a. 25 II. 20 III. 15 IV. 10 V. 5

          13. Consider the linear DE $xy' = \frac{x^2 + xy}{x + y}$. Which value of a and b, the given DE will be homogenous?
I. $a = 0$ and $b = 1$
II. $a = 1$ and $b = 0$
III. $a = 1$ and $b = 2$
IV. $a = 2$ and $b = 1$

14. The roots of the characteristic equation of the third order homogenous DE is $r_1 = 0, r_2 = 1, r_3 = 1$. The general solution of the given DE is
I. $y = c_1e^x + c_2e^x + c_3$
II. $y = c_1e^x + c_2xe^x + c_3$
III. $y = c_1e^x + c_2x^2e^x + c_3x$
IV. $y = c_1e^x + c_2e^x + c_3x$
V.

15. According to the drag equation the velocity of an object moving through a fluid can be modeled by the equation $y' = -ky$ where k is constant. An object moving through the water has an initial velocity of 40 m/s. One seconds later, the velocity has 30 m/s. What will the velocity in m/s be nineth seconds?
a. 25
II. 20
III. 15
IV. 10
V. 5

13. Consider the linear DE xy' = (x^2 + xy)/(x + y). Which value of a and b, the given DE will be homogenous?
I. a = 0 and b = 1
II. a = 1 and b = 0
III. a = 1 and b = 2
IV. a = 2 and b = 1

14. The roots of the characteristic equation of the third order homogenous DE is r1 = 0, r2 = 1, r3 = 1. The general solution of the given DE is
I. y = c1e^x + c2e^x + c3
II. y = c1e^x + c2xe^x + c3
III. y = c1e^x + c2x^2e^x + c3x
IV. y = c1e^x + c2e^x + c3x
V.

15. According to the drag equation the velocity of an object moving through a fluid can be modeled by the equation y' = -ky where k is constant. An object moving through the water has an initial velocity of 40 m/s. One seconds later, the velocity has 30 m/s. What will the velocity in m/s be nineth seconds?
a. 25
II. 20
III. 15
IV. 10
V. 5

Added by Alexander M.

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