Daily Practice Problems

Class 12 Maths

Differential Equations

Class 12 Maths

Differential Equations

**Question 1:**

Determine order and degree (if defined) of differential equation (y′′′)^{2} + (y″)^{3} + (y′)^{4} + y^{5} = 0

**Question 2:**

Solve the differential equation: (x^{2} - 1) * dy/dx + 2xy = 2/(x^{2} - 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 – y^{2})/(1 – x^{2})} = 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 (x^{2} - y^{2}) = c(x^{2} - y^{2})^{2} is the general solution of differential equation

(x^{3} – 3xy^{2})dx = (y^{3} – 3x^{2}y)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 d^{2}y/dx^{2} + 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 + y^{2})/(1 + x^{2}).

**Question 14:**

Integrating factor of the differential equation (1 – x^{2})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 + x^{2}) : y’ = xy/(1 + x^{2})

**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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