Science (English Medium) कक्षा १२ - CBSE Important Questions for Mathematics

Write the integrating factor of the following differential equation:

(1+y²) dx−(tan⁻¹ y−x) dy=0

Find the the differential equation for all the straight lines, which are at a unit distance from the origin.

Show that the differential  equation `2xydy/dx=x^2+3y^2`  is homogeneous and solve it.

Find the particular solution of differential equation:

`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`

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

Find the integrating factor for the following differential equation:`x logx dy/dx+y=2log x`

Find the particular solution of the differential equation `(1+x^2)dy/dx=(e^(mtan^-1 x)-y)` , give that y=1 when x=0.

Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.

Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.

Find the particular solution of the differential equation x (1 + y²) dx – y (1 + x²) dy = 0, given that y = 1 when x = 0.

For the differential equation, find the general solution:

sec² x tan y dx + sec² y tan x dy = 0

Which of the following is a homogeneous differential equation?

Solve the differential equation  `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`

Solve the differential equation `(tan^(-1) x- y) dx = (1 + x^2) dy`

Find the general solution of the differential equation `dy/dx - y = sin x`

For the curve y = 5x – 2x³, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3

if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`

Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by  x² - y² = cx

Find the particular solution of the differential equation

`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`

Solve the following differential equation:
\[\text{ cosec }x \log y \frac{dy}{dx} + x^2 y^2 = 0\]