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

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = e^−2x (A cos x + B sin x)

Form the differential equation of family of lines having intercepts a and b on the co-ordinate ares respectively.

Find the differential equation all parabolas having a length of latus rectum 4a and axis is parallel to the axis.

Find the differential equation of the ellipse whose major axis is twice its minor axis.

Find the differential equation of all circles having radius 9 and centre at point (h, k).

Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.

Form the differential equation of all parabolas whose axis is the X-axis.

In the following example verify that the given expression is a solution of the corresponding differential equation:

xy = log y +c; `"dy"/"dx" = "y"^2/(1 - "xy")`

In the following example verify that the given expression is a solution of the corresponding differential equation:

y = `(sin^-1 "x")^2 + "c"; (1 - "x"^2) ("d"^2"y")/"dx"^2 - "x" "dy"/"dx" = 2`

In the following example verify that the given expression is a solution of the corresponding differential equation:

y = e^-x + Ax + B; `"e"^"x" ("d"^2"y")/"dx"^2 = 1`

In the following example verify that the given expression is a solution of the corresponding differential equation:

y = x^m; `"x"^2 ("d"^2"y")/"dx"^2 - "mx" "dy"/"dx" + "my" = 0`

In the following example verify that the given expression is a solution of the corresponding differential equation:

y = `"a" + "b"/"x"; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0`

In the following example verify that the given expression is a solution of the corresponding differential equation:

y = `"e"^"ax"; "x" "dy"/"dx" = "y" log "y"`

Solve the following differential equation:

`"dy"/"dx" = (1 + "y")^2/(1 + "x")^2`

Solve the following differential equation:

`log  ("dy"/"dx") = 2"x" + 3"y"`

Solve the following differential equation:

`"y" - "x" "dy"/"dx" = 0`

Solve the following differential equation:

`"sec"^2 "x" * "tan y"  "dx" + "sec"^2 "y" * "tan x"  "dy" = 0` 

Solve the following differential equation:

cos x . cos y dy − sin x . sin y dx = 0

Solve the following differential equation:

`"dy"/"dx" = - "k",` where k is a constant.

Solve the following differential equation:

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