Home
Class 11
MATHS
Find a positive real valued continuously...

Find a positive real valued continuously differentiable functions f on the real line such that for all x `f^2(x)=int_0^x((f(t))^2+(f^(prime)(t))^2)dt+e^2`

Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) be a continuous and differentiable function such that f(x)=int_0^xsin(t^2-t+x)dt Then prove that f^('')(x)+f(x)=cosx^2+2xsinx^2

Let f(x) be a continuous and differentiable function such that f(x)=int_0^xsin(t^2-t+x)dt Then prove that f^('')(x)+f(x)=cosx^2+2xsinx^2

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

f(x)=int_0^x e^t f(t)dt+e^x , f(x) is a differentiable function on x in R then f(x)=

Let f(x) be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then int_(0)^(1)f(x)dx=

Let f be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then prove that f(x)=(x^(3))/(3)+x^(2)

A function f(x) satisfies f(x)=sinx+int_0^xf^(prime)(t)(2sint-sin^2t)dt is

A function f(x) satisfies f(x)=sinx+int_0^xf^(prime)(t)(2sint-sin^2t)dt is