HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Solve the following differential equation.

`(dθ)/dt  = − k (θ − θ_0)`

Solve the following differential equation.

`y^3 - dy/dx = x dy/dx`

For each of the following differential equations find the particular solution.

(x − y² x) dx − (y + x² y) dy = 0, when x = 2, y = 0

For the following differential equation find the particular solution.

`(x + 1) dy/dx − 1 = 2e^(−y)`,

when y = 0, x = 1

For each of the following differential equations find the particular solution.

`y (1 + logx)dx/dy - x log x = 0`,

when x=e, y = e².

For  the following differential equation find the particular solution.

`dy/ dx = (4x + y + 1),

when  y = 1, x = 0

Solve the following differential equation.

xdx + 2y dx = 0

Solve the following differential equation.

y² dx + (xy + x² ) dy = 0

Solve the following differential equation.

x²y dx − (x³ + y³) dy = 0

Solve the following differential equation.

`dy /dx +(x-2 y)/ (2x- y)= 0`

Solve the following differential equation.

(x² − y² ) dx + 2xy dy = 0

Solve the following differential equation.

`xy  dy/dx = x^2 + 2y^2`

Find the equation of tangent and normal to the curve at the given points on it.

y = 3x² - x + 1 at (1, 3)

Find the equation of tangent and normal to the curve at the given points on it.

2x² + 3y² = 5 at (1, 1)

Find the equation of tangent and normal to the curve at the given points on it.

x² + y² + xy = 3 at (1, 1)

Find the equations of tangent and normal to the curve y = x² + 5 where the tangent is parallel to the line 4x − y + 1 = 0.

Find the equations of tangent and normal to the curve y = 3x² - 3x - 5 where the tangent is parallel to the line 3x − y + 1 = 0.

Solve the following differential equation.

`x^2 dy/dx = x^2 +xy - y^2`

Solve the following differential equation.

`dy/dx + y = e ^-x`

Solve the following differential equation.

`dy/dx + y` = 3