Advertisements
Advertisements
Question
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Advertisements
Solution
`(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
RELATED QUESTIONS
Solve the following differential equation:
`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0
Solve the following differential equation:
x cos y dy = ex(x log x + 1) dx
Choose the correct alternative:
The number of arbitrary constants in the general solutions of order n and n +1are respectively
Solve: (1 – x) dy – (1 + y) dx = 0
Solve the following homogeneous differential equation:
(y2 – 2xy) dx = (x2 – 2xy) dy
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`
Choose the correct alternative:
The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is
Solve `x ("d"y)/(d"x) + 2y = x^4`
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
