Home
Class 12
MATHS
Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^...

Let `y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0)=0,x in R ,` where `f^(prime)(x)` denotes `(dy(x))/(dx),` and `g(x)` is a given non-constant differentiable function on `R` with `g(0)=g(2)=0.` Then the value of `y(2)` is______

Promotional Banner

Similar Questions

Explore conceptually related problems

Let y'(x)+g'(x)/(g(x))y(x)=g'(x)/(1+(g(x))^(2)) where f'(x) denotes d(f(x))/(d)(x) and g(x) is given non constant differentiable function on R.If g(1)=y(1)=1 and g(e)=sqrt(2e-1) then y(e) equals

f and g differentiable functions of x such that f(g(x))=x," If "g'(a)ne0" and "g(a)=b," then "f'(b)=

Let g:R rarr R be a differentiable function satisfying g(x)=g(y)g(x-y)AA x,y in R and g'(0)=a and g'(3)=b. Then find the value of g'(-3)

Let g^(prime)(x)>0a n df^(prime)(x)<0AAx in Rdot Then (f(x+1))>g(f(x-1)) f(g(x-1))>f(g(x+1)) g(f(x+1))

Let x=f(t) and y=g(t), where x and y are twice differentiable function. If f'(0)= g'(0) =f''(0) = 2. g''(0) = 6, then the value of ((d^(2)y)/(dx^(2)))_(t=0) is equal to

If f(x) and g(x) are two differentiable functions on R^+ such that xf'(x)+g(x)=0 and xg'(x)+f(x)=0 for all x in R^+and f(1)+g(1)=4, then the value of f"(2).g"(2) is

Let f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x)AA x,y in R where g(x) is continuous then f'(x) is

Let y=f(x) and y=g(x) be two monotonic, bijective functions such that f(g(x) is defined than y=f(g(x)) is