Differential Equation 01

Which of the following is a differential equation of the first order, first degree ODE?

• linear, homogenous and first order

• linear, homogeneous and first order

• linear, second order and nonhomogeneous

• linear, homogeneous, and second order

• linear, second order, nonhomogeneous

• linear, second order, homogeneous

• nonlinear, second order, homogeneous

• nonlinear, second order, nonhomogeneous

Find the differential equations of the family of lines passing through the origin.

• x dy – y dx = 0

• x dy + y dx = 0

• y = mx + b

• y’ = x

Write the differential equation of straight lines with slope and y-intercept equal.

• y dx + (x – 1) dy = 0

• y dx – (x + 1) dy = 0

• x dy – (y + 1) dx = 0

• y dy + (x + 1) dx = 0

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis?

• 2x dx + y dy = 0

• 2x dy – y dx = 0

• 4x dy + x dx = 0

• 3x dy + 2y dx = 0

What is the differential equation of circle whose center is at the origin?

• x dy – y dx = 0

• x dx + y dy = 0

• y”(x – 1) – xy’ + y = 0

• y’(x + 1) + xy’ + x = 0

• y”(x – 1) + xy’ + y = 0

• y’(x + 1) +xy +x = 0

• 46

• 64

• 54

• 120

Find the general solution of 𝑦′ = 𝑦 sec⁡𝑥.

• y = C(sec x – tan x)

• y = C(sec x + tan x)

• y = C(sec 2x + tan x)

• y = C(tan x – sec x)