मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

State whether the following statement is True or False: A differential equation in which the dependent variable, say y, depends only on one independent variable, say x, is called as ordinary - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

State whether the following statement is True or False:

A differential equation in which the dependent variable, say y, depends only on one independent variable, say x, is called as ordinary differential equation

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

True

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.3

संबंधित प्रश्‍न

For the differential equation, find the general solution:

sec2 x tan y dx + sec2 y tan x dy = 0


For the differential equation, find the general solution:

(ex + e–x) dy – (ex – e–x) dx = 0


For the differential equation, find the general solution:

ex tan y dx + (1 – ex) sec2 y dy = 0


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

`cos (dx/dy) = a(a in R); y = 1` when x = 0


Find the equation of a curve passing through the point (0, -2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point.


Find the particular solution of the differential equation:

`y(1+logx) dx/dy - xlogx = 0`

when y = e2 and x = e


Find the particular solution of the differential equation `dy/dx + 2y tan x = sin x` given that y = 0 when x =  `pi/3`


Solve the differential equation `"dy"/"dx" = 1 + "x"^2 +  "y"^2  +"x"^2"y"^2`, given that y = 1 when x = 0.


Solve the differential equation:

`dy/dx = 1 +x+ y + xy`


Solve

`y log  y dy/dx + x  – log y = 0`


The resale value of a machine decreases over a 10 year period at a rate that depends on the age of the machine. When the machine is x years old, the rate at which its value is changing is ₹ 2200 (x − 10) per year. Express the value of the machine as a function of its age and initial value. If the machine was originally worth ₹1,20,000, how much will it be worth when it is 10 years old?


Find the solution of `"dy"/"dx"` = 2y–x.


Solve the differential equation `(x^2 - 1) "dy"/"dx" + 2xy = 1/(x^2 - 1)`.


Solve the differential equation `"dy"/"dx" + 1` = ex + y.


Solve: (x + y)(dx – dy) = dx + dy. [Hint: Substitute x + y = z after seperating dx and dy]


Solve the following differential equation

x2y dx – (x3 + y3)dy = 0


A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some virus. Assume that the rate at which the virus spreads is directly proportional to the product of the number of infected students and the number of non-infected students. If the number of infected students on 4th day is 30, then number of infected studetns on 8th day will be ______.


The solution of the differential equation, `(dy)/(dx)` = (x – y)2, when y (1) = 1, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×