Home
Class 12
MATHS
x(dy)/(dx)-y=2sqrt(y^2-x^2)...

`x(dy)/(dx)-y=2sqrt(y^2-x^2)`

Text Solution

Verified by Experts

The correct Answer is:
`y+sqrt(y^(2)-x^(2))=C|x|^(3)`
`int1/(sqrt(v^(2)-1))dv=int2/xdx rArr log|v+sqrt(v^(2)-1)|=2log|x|+log|C_(1)|`.
Promotional Banner

Topper's Solved these Questions

  • HOMOGENEOUS DIFFERENTIAL EQUATION

    RS AGGARWAL|Exercise Exercise 20|30 Videos

  • FUNDAMENTAL CONCEPTS OF 3-DIMENSIONAL GEOMETRY

    RS AGGARWAL|Exercise Exercise|18 Videos

  • INDEFINITE INTEGRAL

    RS AGGARWAL|Exercise Objective Questions|41 Videos

Similar Questions

Explore conceptually related problems

solve x(dy)/(dx)-y=sqrt(x^(2)+y^(2))

If y=sqrt(x)+(1)/(x), Show that 2x(dy)/(dx)+y=2sqrt(x)

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

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

General solution of differential equation x^(2)(x+y(dy)/(dx))+(x(dy)/(dx)-y)sqrt(x^(2)+y^(2))=0 is

x(dy)/(dx)=y+sqrt(x^(2)-y^(2)), where (y)/(x)=b

If y=sqrt(x)+(1)/sqrt(x) , then show that 2x(dy)/(dx)+y=2sqrt(x) .

For each of the following differential equations verify that the accompanying functions a solution.Differential Function x(dy)/(dx)=yy=axx+y(dy)/(dx)=0y=+-sqrt(a^(2)-x^(2))x(dy)/(dx)y=y^(2)y=(a)/(x+a)x^(3)(d^(2)y)/(dx^(2))=1y=ax+b+(1)/(2x)y=((dy)/(dx))^(2)y=(1)/(4)(x+-a)^(2)

(y)/(x)(dy)/(dx)=sqrt(1+x^(2)+y^(2)+x^(2)y^(2))