Advertisements
Advertisements
प्रश्न
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Advertisements
उत्तर
`(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
`(1 + x^2)/x "d"x = (1 + y)y "d"y`
`(1/x + x^2/x) "d"x = (y + y^2) "d"y`
⇒ `[1/x + x] "d"x = (y + y^2) "d"y`
Differentiating on both sides
`int (1/x + x) "d"x = int (y + y^2) "d"y`
⇒ `log x + x^2/2 = y^2/2 + y^3/3 + "c"`
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation:
`y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y`
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 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:
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)/("d"x) + y tan x = cos^3x`
Choose the correct alternative:
The differential equation of y = mx + c is (m and c are arbitrary constants)
Choose the correct alternative:
Solution of `("d"x)/("d"y) + "P"x = 0`
Form the differential equation having for its general solution y = ax2 + bx
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
