Home
Class 12
MATHS
Solve the following differential equatio...

Solve the following differential equation: `\ x(dy)/(dx)-y=2\ sqrt(y^2-x^2)`

Text Solution

Verified by Experts

The correct Answer is:
`1/2log_(e)y+sqrt(y^(2)-x^(2))/(x)=log_(e)cx`
Putting `y=vx` and `(dy)/(dx)=v+x(dv)/(dx)`, we get
`xv+x^(2)(dv)/(dx)=vx+2xsqrt(v^(2)-1)`
or `int(dv)/(2sqrt(v^(2)-1))=int(dx)/x`,
Integrating, we get
`1/2" ln "(v+sqrt(v^(2)-1))="ln "cx`
or `1/2"ln "(y+sqrt(y^(2)-x^(2)))/x="ln "cx`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Solve the following differential equations : dy/dx+sqrt((1-y^2)/(1-x^2))=0

Solve the following differential equation xdy-ydx=sqrt(x^(2)+y^(2))dx

Solve the following differential equations: dy/dx=e^(x+y)+x^2 e^y

Solve the following differential equations: (xy^2+x)dx+(yx^2+y)dy=0

Solve the differential equation : (dy)/(dx)-y/x=2x^2

Solve the following differential equations : x(1+y^2)dx+y(1+x^2)dy=0,at, x=0,y=1

Find the order and degree, if defined, of each of the following differential equations: (i) (dy)/(dx) - cos x = 0 (ii) xy (d^(2)y)/(dx^(2)) + x((dy)/(dx))^(2) - y (dy)/(dx) = 0 (iii) y''' + y^(2) + e^(y)' = 0

Solve the differential equation (x)dy = ( 1 + y^(2))dx .

Find the general solution of the differential equation (dy)/(dx) + sqrt((1 - y^(2))/(1 - x^(2))) = 0 .

The solution of the differential equation (dy)/(dx)=e^(2x+y) is