Home
Class 12
MATHS
Solve (dy)/(dx) = yf^(')(x) = f(x) f^(')...

Solve `(dy)/(dx) = yf^(')(x) = f(x) f^(')(x)`, where `f(x)` is a given integrable function of `x`.

Text Solution

Verified by Experts

The correct Answer is:
`log_(e)(1+y-f(x))+f(x)+c=0`
`(dy)/(dx)+yf^(')(x)=f(x)f^(')(x)`
or `(dy)/(dx)=[f(x)-y]f^(')(x)`
Put `f(x)-y=t`
`therefore f^(')(x) = (dy)/(dx)=(dt)/(dx)`
Then the given equation transforms to
`f^(')(x)-(dt)/(dx)=(dt)/(dx)`
or `int(dt)/(1-t)=intf^(')(x)dx`
or `-log[1+y-f(x)]+f(x)+c=0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.4|6 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.5|7 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.2|6 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

Solve: (dy)/(dx)+y*f'(x)=f(x)*f'(x), where f(x) is a given function.

Solve: (dy)/(dx) = (yf^(')(x)-y^(2))/(f(x))

Solve: dy/dx=(y f\'(x)-y^2)/f(x) , where f(x) is a given function of x

Solve (dy)/(dx)+y phi'(x)=phi(x).phi'(x), "where" " "phi(x) is a given function.

If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x) , then f(x) is, (given f(0) = 0)

dy/dx+y f\'(x)-f(x)f\'(x)=0

A function f satisfies the condition f(x)=f'(x)+f''(x)+f''(x)+…, where f(x) is a differentiable function indefinitely and dash denotes the order the derivative. If f(0) = 1, then f(x) is

The solution of (dy)/(dx)+yf'(x)-f(x).f'(x)=0,y!=f(x) is

int ((x ^(2) -x+1)/(x ^(2) +1)) e ^(cot^(-1) (x))dx =f (x) .e ^(cot ^(-1)(x)) +C where C is constant of integration. Then f (x) is equal to: