हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा १२

Solve the following differential equation: dddydx=1-y21-x2 - Mathematics

Advertisements
Advertisements

प्रश्न

Solve the following differential equation:

`("d"y)/("d"x) = sqrt((1 - y^2)/(1 - x^2)`

योग
Advertisements

उत्तर

The equation can be written as

`("d"y)/sqrt(1 - y^2) = ("d"x)/sqrt(1 - x^2)`

Taking Integration on both sides, we get

`int ("d"y)/sqrt(1 - y^2) = int ("d"x)/sqrt(1 - x^2)`

sin–1y = sin1x + C

shaalaa.com
Solution of First Order and First Degree Differential Equations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 10: Ordinary Differential Equations - Exercise 10.5 [पृष्ठ १६१]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 10 Ordinary Differential Equations
Exercise 10.5 | Q 4. (i) | पृष्ठ १६१

संबंधित प्रश्न

Solve the following differential equation:

`x ("d"y)/("d"x) = y - xcos^2(y/x)`


Choose the correct alternative:

The solution of `("d"y)/("d"x) + "p"(x)y = 0` is


Solve: `("d"y)/("d"x) = "ae"^y`


Solve: ydx – xdy = 0 dy


Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`


Solve: (1 – x) dy – (1 + y) dx = 0


Solve: `("d"y)/("d"x) = y sin 2x`


Find the curve whose gradient at any point P(x, y) on it is `(x - "a")/(y - "b")` and which passes through the origin


Solve the following homogeneous differential equation:

`x ("d"y)/("d"x) = x + y`


Solve the following homogeneous differential equation:

The slope of the tangent to a curve at any point (x, y) on it is given by (y3 – 2yx2) dx + (2xy2 – x3) dy = 0 and the curve passes through (1, 2). Find the equation of the curve


Solve the following:

`("d"y)/(""dx) + y cos x = sin x cos x`


Solve the following:

`x ("d"y)/("d"x) + 2y = x^4`


Solve the following:

`("d"y)/("d"x) + y/x = x'e"^x`


Choose the correct alternative:

A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution


Choose the correct alternative:

A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution


A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ’m’ of intervals between overhauls by the equation `"m"^2 "dC"/"dm" + 2"mC"` = 2 and c = 4 and when  = 2. Find the relationship between C and m


Solve (D2 – 3D + 2)y = e4x given y = 0 when x = 0 and x = 1


Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×