HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`

Solve the differential equation xdx + 2ydy = 0

Solve the differential equation (x² – yx²)dy + (y² + xy²)dx = 0

Solve the following differential equation `("d"y)/("d"x)` = x²y + y

Solve: `("d"y)/("d"x) + 2/xy` = x² 

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

Solve the following differential equation

`yx ("d"y)/("d"x)` = x² + 2y² 

Solve the following differential equation y log y = `(log  y - x) ("d"y)/("d"x)`

For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0

Solve the following differential equation y²dx + (xy + x²) dy = 0

Solve the following differential equation

`x^2  ("d"y)/("d"x)` = x² + xy − y² 

Solve the differential equation

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

If A = `[(3, -1),(4, 2)]`, B = `[(2),(-1)]`, find X such that AX = B.

Solve the differential equation

`x + y dy/dx` = x² + y²

If A = `[(cosθ, -sinθ, 0),(sinθ, cosθ, 0),(0, 0, 1)]`, find A^–1

Find the matrix X such that AX = B, where A = `[(2, 1),(-1, 3)]`, B = `[(12, -1),(1, 4)]`.

Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`

Order and degree of the differential equation `[1+(dy/dx)^3]^(7/3)=7(d^2y)/(dx^2)` are respectively 

(A) 2, 3

(B) 3, 2

(C) 7, 2

(D) 3, 7

Find the combined equation of the following pair of lines:

2x + y = 0 and 3x − y = 0