Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
`(ydx - xdy) cot (x/y)` = ny2 dx
Advertisements
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")`
APPEARS IN
संबंधित प्रश्न
Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)
Solve the following differential equation:
(ey + 1)cos x dx + ey sin x dy = 0
Solve the following differential equation:
`(x^3 + y^3)"d"y - x^2 y"d"x` = 0
Solve the following differential equation:
`y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y`
Solve the following differential equation:
`x ("d"y)/("d"x) = y - xcos^2(y/x)`
Solve the following differential equation:
(x2 + y2) dy = xy dx. It is given that y (1) = y(x0) = e. Find the value of x0
Choose the correct alternative:
The solution of `("d"y)/("d"x) + "p"(x)y = 0` is
Choose the correct alternative:
The number of arbitrary constants in the general solutions of order n and n +1are respectively
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) - y = sqrt(x^2 + y^2)`
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:
`("d"y)/("d"x) + y/x = x"e"^x`
Choose the correct alternative:
If y = ex + c – c3 then its differential equation is
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is
Choose the correct alternative:
The differential equation of y = mx + c is (m and c are arbitrary constants)
Choose the correct alternative:
A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is
Solve x2ydx – (x3 + y3) dy = 0
