Home
Class 12
MATHS
Verify that the given functions (explic...

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:`y=sqrt(1+x^2)` : `yprime=(x y)/(1+x^2)`

Text Solution

Verified by Experts

Given, `y=sqrt(1+x^(2))`
`implies y'=(2x)/(2sqrt(1+x^(2)))`
`=(x)/(sqrt(1+x^(2)))=(xsqrt(1+x^(2)))/(1+x^(2))`
`=(xy)/(1+x^(2))`
Therefore, `y=sqrt(1+x^(2))` is a solution of given differential equation.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9.3|12 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9.4|23 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9.1|12 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|44 Videos

Similar Questions

Explore conceptually related problems

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=x^2+2x+C : yprime-2x-2=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=cosx+C : yprime+sinx=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=cosx+C : yprime+sinx=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : y=Ax : xy'=y(x ne 0)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=e^x+1:yprimeprime-yprime=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=e^x+1:yprimeprime-yprime=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: x+y=tan^(-1)y : y^2y^(prime)+y^2+1=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: x y = log y + C : yprime=(y^2)/(1-x y)(x y!=1)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=sqrt(a^2-x^2)x in (-x , a) : x+y(dy)/(dx)=0(y!=0)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=sqrt(a^2-x^2)x in (-x , a) : x+y(dy)/(dx)=0(y!=0)