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Express x dy-y dx=sqrt(x^(2)+y^(2)) dx i...

Express `x dy-y dx=sqrt(x^(2)+y^(2)) dx` in the form `F((y)/(x))=(dy)/(dx)` .

Text Solution

Verified by Experts

The correct Answer is:
`(y)/(x)+sqrt(1+((y)/(x))^(2))`
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Express (x sqrt(x^(2)+y^(2))-y^(2))dx+xy dy=0 in the form (dy)/(dx)=F((y)/(x)) .

(i) Express (x+sqrt(x^(2) + y^(2)) - y^(2)) dx+ xydy = 0 in the form (dy)/(dx) = F((y)/(x)) (ii) Express the differental equation xydx + x^(2)dy - ysqrt(x^(2) + y^(2))dy = 0 in the form (dx)/(dy) = F((x)/(y))

Knowledge Check

  • The solution of x dy - y dx = sqrt(x^(2) + y^(2)) dx is

    A
    `y + sqrt(x^(2) + y^(2)) = cy^(2)`
    B
    `y + sqrt(x^(2) + y^(2)) = cx^(2)`
    C
    `y + sqrt(x^(2) - y^(2)) = cx^(2)`
    D
    `y- sqrt(x^(2) + y^(2)) = vx^(2)`

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    Express (dy)/(dx)=(y)/(x+ye^((-2x)/(y))) in the form (dx)/(dy)=F((x)/(y)).

    (dy)/(dx) + (y)/(x) = x^(2)

    Express the following differential equations in the form (dy)/(dx) = F((y)/(x)) . (i) xdy - ydx = sqrt(x^(2) + y^(2))dx (ii) [x - y Tan^(-1)((y)/(x))] dx + x Tan^(-1)((y)/(x)) dy = 0 (iii) xdy = y(log y - log x+1)dx

    y dx + (x - y^(2))dy = 0

    y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

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