Home
Class 12
MATHS
If y=xlog"{"x/((a+b x))"]" , then show t...

If `y=xlog"{"x/((a+b x))"]"` , then show that `x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2dot`

Text Solution

AI Generated Solution

To solve the problem, we start with the given equation: \[ y = x \log\left(\frac{x}{a + b x}\right) \] ### Step 1: Rewrite the equation using logarithmic properties Using the property of logarithms, we can rewrite the equation: ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Solved Examples|28 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

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

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2

If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .

If y=3cos(logx)+4sin(logx),\ then show that x^2(d^2\ y)/(dx^2)+x(dy)/(dx)+y=0

If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^2 y(dy)/(dx)-x (d) (y(dy)/(dx)-x)^2

(dy)/(dx)=(x+y+1)/(2x+2y+3)

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