Home
Class 12
MATHS
Solve the equation (1-x^2)((dy)/(dx))+2x...

Solve the equation `(1-x^2)((dy)/(dx))+2x y=xsqrt(1-x^2)`

Text Solution

Verified by Experts

The correct Answer is:
`y=sqrt(1-x^(2))+c(1-x^(2))`
We have
`(dy)/(dx)+(2x)/(1-x^(2))y=x/sqrt(1-x^(2))`
Here, `P=(2x)/(1-x^(2))` and `q=x/sqrt(1-x^(2))`
`I.F. e^(int(2x)/(1-x^(2))dx)=e^(-log(1-x^(2)))=1/(1-x^(2))`
Therefore, the solution is
`y/(1-x^(2))=int(x)/sqrt((1-x^(2)) xx 1/(1-x^(2))dx+c`
`=1/sqrt(1-x^(2))+c`
or `y=sqrt(1-x^(2))+c(1-x^(2))`
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 equation (x+y+1)((dy)/(dx))=1

Solve the equation (dy)/(dx)+(x y)/((1-x^2))=xsqrt(y)

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

Solve the equation (dy)/(dx)=y/(2ylogy+y-x)

solve the differential equation (1+x^2)dy/dx=x

The solution of the equation (dy)/(dx)=sqrt(1-x^(2)-y^(2)+x^(2)y^(2)) is -

Solve: (1+x^2)(dy)/(dx) = y+tan^(-1)x

The solution of the differential equation x(x^2+1)((dy)/(dx))=y(1-x^2)+x^3logx is

Solve: (x^2-1)(dy)/(dx) + 2xy = 2/(x^2-1)

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