Question 1:

Determine order and degree (if defined) of differential equation (y′′′)² + (y″)³ + (y′)⁴ + y⁵ = 0

 

Question 2:

Solve the differential equation: (x² - 1) * dy/dx + 2xy = 2/(x² - 1)

 

Question 3:

Form the differential equation representing the family of curves

y = a sin(x + b), where a, b are arbitrary constants.

 

Question 4:

Find the general solution of the differential equation dy/dx + √{(1 – y²)/(1 – x²)} = 0

 

Question 5:

Find the differential equation of the family of lines through the origin.

 

Question 6:

Find a particular solution of the differential equation (x - y)(dx + dy) = dx – dy, given that y = -1, when x = 0.

 

Question: 7

Form the differential equation representing the family of curves

y = a sin(3x – b), where a and b are arbitrary constants.

 

Question 8:

Find the general solution of the differential equation

cos(dy/dx) = a (a ∈ R); y = 1 when x = 0.

 

Question 9:

Find the general solution of the differential equation:

x * dy/dx + y – x + xy cot x = 0 (x ≠ 0)

 

Question 10:

Prove that (x² - y²) = c(x² - y²)² is the general solution of differential equation

(x³ – 3xy²)dx = (y³ – 3x²y)dy, where c is a parameter.

 

Question 11:

Verify that the function y = a cos x + b sin x, where, a, b ∈ R is a solution of the differential equation d²y/dx² + y = 0.

 

Question 12:

For each of the given differential equation, find a particular solution satisfying the given condition: dy/dx = y * tan x; y = 1 when x = 0

 

Question 13:

Find the general solution of the differential equation dy/dx = (1 + y²)/(1 + x²).

 

Question 14:

Integrating factor of the differential equation (1 – x²)dy/dx – xy = 1 is ____.

 

Question 15:

Determine order and degree (if defined) of differential equation

y’’’ + 2y’’ + y’ = 0

 

Question 16:

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y = √(1 + x²)                 :                 y’ = xy/(1 + x²)

 

Question 17:

Solve: cos(dy/dx) = a (a ∈ R); y = 1 when x = 0

 

Question 18:

Solve: dy/dx = 1 + x + y + xy

 

Question 19:

Write the general solution of differential equation:

dy/dx = e^x+y

 

Question 20:

Form the differential equation representing the family of curves:

y = e^2x(a + bx), where ‘a’ and ‘b’ are arbitrary constants.

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