HSC Science (Electronics) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

Solve the following differential equation:

`"y"^3 - "dy"/"dx" = "x"^2 "dy"/"dx"`

Solve the following differential equation:

`2"e"^("x + 2y") "dx" - 3"dy" = 0`

Solve the following differential equation:

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

For the following differential equation find the particular solution satisfying the given condition:

3e^x tan y dx + (1 + e^x) sec² y dy = 0, when x = 0, y = π.

For the following differential equation find the particular solution satisfying the given condition:

`y(1 + log x) dx/dy - x log x = 0, y = e^2,` when x = e

For the following differential equation find the particular solution satisfying the given condition:

`(e^y + 1) cos x + e^y sin x. dy/dx = 0,  "when" x = pi/6,` y = 0

For the following differential equation find the particular solution satisfying the given condition:

`("x" + 1) "dy"/"dx" - 1 = 2"e"^-"y" , "y" = 0`, when x = 1

For the following differential equation find the particular solution satisfying the given condition:

`cos("dy"/"dx") = "a", "a" ∈ "R", "y"(0) = 2`

Reduce the following differential equation to the variable separable form and hence solve:

`"dy"/"dx" = cos("x + y")`