Linear differential equations of first order first degree Quiz

Question 1: Solve the exact differential equation (x^2 + y^2)dx + 2xydy = 0

• x^2 - y^2 = C

• x^2 + y^2 = 2C

• The exact solution for the given differential equation is x^2 + y^2 = C, where C is the constant of integration.

• x^2 + 2y^2 = C

Question 2: Find the integrating factor for the differential equation (2x + y)dx + (x - y)dy = 0

• 2x + y

• x - y

• e^(2x - y)

• e^(-y)

Question 3: Solve the homogeneous differential equation y' = (2x + 3y) / (x - 2y)

• y = Ce^(3x/2) - (2x/3)

• y = Ce^(5x/2) - (3x/2)

• y = Ce^(5x/2) + (3x/2)

• y = Ce^(4x/2) - (3x/2)

Question 4: Determine the integrating factor for the Bernoulli differential equation y' - 2xy = x^2y^2

• 2x

• e^(2x)

• e^(x^2)

• y^2

Question 5: Solve the homogeneous differential equation xdy - ydx = x^2y^2

• y = -1/x

• y = x

• y = x^2

• y = 1/x

Question 6: Find the integrating factor for the differential equation (3x + 2y)dx + (x - y)dy = 0

• e^(∫3dx) = e^(3x)

• e^(∫-ydx) = e^(-yx)

• e^(∫2dx) = e^(2x)

• e^(∫x^2dx) = e^(x^2)

Question 7: Solve the exact differential equation (2x + y)dx + (x - y)dy = 0

• The exact solution is x^2 + xy + y^2 = C

• The exact solution is 2x^2 - xy + y^2 = C

• The exact solution is x^2 - 2xy + y^2 = C

• The exact solution is x^2 - xy + y^2 = C, where C is the constant of integration.

Question 8: Determine the integrating factor for the Bernoulli differential equation y' - 3xy = x^2y^2

• e^(2x^3)

• e^(x^2)

• e^(4x)

• e^(3x^2/2)

Question 9: Solve the differential equation (x^2 + y^2)dx + 2xydy = 0 by reducing it to a linear differential equation

• y = x^2 - C

• The answer is not provided as it requires a step-by-step explanation to solve the given differential equation.

• y = x^2 + C

• y = x^2 + Cx

Question 10: Solve the differential equation xdy - ydx = x^2y^2 by reducing it to a linear differential equation

• y = x^3

• y = x^2

• y = x^4

• y = vx