हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा १२

Solve the following differential equation: (ydx-xdy)cot(xy) = ny2 dx - Mathematics

Advertisements
Advertisements

प्रश्न

Solve the following differential equation:

`(ydx - xdy) cot (x/y)` = ny2 dx

योग

उत्तर

`(ydx - xdy) cot (x/y)` = ny2 dx

Dividing throughout by 'y2'

`((ydx - xdy)/y^2) cot (x/y)` = n dx

`"d"(x/y)* cot(x/y)` = n dx

`int cot(x/y)* "d"(x/y) = "n" int  "d"x`

`log sin(x/y)` = nx + c

`sin(x/y) = "e"^("n"x  +  "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 १६२]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 10 Ordinary Differential Equations
Exercise 10.5 | Q 4. (vi) | पृष्ठ १६२

संबंधित प्रश्न

The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x


Solve the following differential equation:

`y"d"x + (1 + x^2)tan^-1x  "d"y`= 0


Solve the following differential equation:

`sin  ("d"y)/("d"x)` = a, y(0) = 1


Solve the following differential equation:

`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0


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


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


Solve the following homogeneous differential equation:

`(x - y) ("d"y)/("d"x) = x + 3y`


Solve the following homogeneous differential equation:

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


Solve the following homogeneous differential equation:

`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`


Solve the following:

If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x


Solve the following:

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


Choose the correct alternative:

The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is


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:

Which of the following is the homogeneous differential equation?


Choose the correct alternative:

The solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is


Form the differential equation having for its general solution y = ax2 + bx


Solve (x2 + y2) dx + 2xy dy = 0


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


Solve x2ydx – (x3 + y3) dy = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×