Home
Class 12
MATHS
xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=...

`xsqrt(1+y)+ysqrt(1+x)=0` then `(dy)/(dx)=`

Text Solution

Verified by Experts

`"We have "xsqrt(1+y)+ysqrt(1+x)=0`
`"or "xsqrt(1+y)=-ysqrt(1+x)`
`"or "x^(2)(1+y)=y^(2)(1+x)" [On squaring both sides]"`
`"or "x^(2)-y^(2)=y^(2)x-x^(2)y`
`"or "(x+y)(x-y)=-xy(x-y)`
`"or "x+y=-xy" "[because x- yne 0" as "x = y" does not satisfy the given equation"]`
`"or "y=-(x)/(1+x)`
`"or "(dy)/(dx)=-{((1+x)xx1-x(0+1))/((1+x^(2)))}=-(1)/((1+x^(2)))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.3|10 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.4|12 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

IF xsqrt(1+y)+ysqrt(1+x)=0 , show that, dy/dx=-1/(1+x)^2

If xsqrt(1+y)+ysqrt(1+x)=0 , prove that dy/dx=(-1)/((1+x)^2

IF xsqrt(1+y)+ysqrt(1+x)=0 , show that, (d^2y)/(dx^2)=2/(1+x)^3 .

If x sqrt(1+y)+y sqrt(1+x)=0 then the value of (dy)/(dx) is -

If x sqrt(1-y^(2))+y sqrt(1-x^(2))=k , then the value of (dy)/(dx) at x=0 is -

xsqrt(1-y^(2))dx+ysqrt(1+x^(2))dy=0

If xsqrt(1+y)+ysqrt(1+x)=0," for ", -1 lt x lt 1 , prove that (dy)/(dx)= -(1)/((1+x)^(2)) .

If xsqrt(1-y^(2))+ysqrt(1-x^(2))=k , find [(d^(2)y)/(dx^(2))]_(x=0)

(x+y+1)(dy)/(dx)=1

Solution of the differential equation (y+xsqrt(x y)(x+y))dx+(ysqrt(x y)(x+y)-x)dy=0 is