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),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______

Topper's Solved these Questions

DIFFERENTIAL EQUATION
ARIHANT MATHS ENGLISH|Exercise Differential Equations Exerise 7 :|1 Videos
DETERMINANTS
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos
DIFFERENTIATION
ARIHANT MATHS ENGLISH|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

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______

int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x))/(f(x)*g(x)){logg(x)-logf(x)} \ dx

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

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(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , write the value of (dy)/(dx) at x=0 .

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0), then the value of g^(prime)(1) is ________

If y=|f(x)g(x)h(x)l m n a b c| , prove that (dy)/(dx)=|f^(prime)(x)g^(prime)(x)h^(prime)(x)l m n a b c| .

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

If y=f(x)=x^3+x^5 and g is the inverse of f find g^(prime)(2)

If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of lim_(x->a)(g(x)f(a)-g(a)f(x))/(x-a) is (a) -5 (b) 1/5 (c) 5 (d) none of these

ARIHANT MATHS ENGLISH-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...
Text Solution
|
A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...
Text Solution
|
Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...
Text Solution
|
Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...
Text Solution
|
Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...
Text Solution
|
Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...
Text Solution
|
If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...
Text Solution
|
Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...
Text Solution
|
Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...
Text Solution
|
Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...
Text Solution
|
If a curve y=f(x) passes through the point (1,-1) and satisfies the di...
Text Solution
|
Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...
Text Solution
|
Let the population of rabbits surviving at a time t be governed by t...
Text Solution
|
At present, a firm is manufacturing 2000 items. It is estimated tha...
Text Solution
|
The population p(t) at time t of a certain mouse species satisfies the...
Text Solution
|
If (dy)/(dx)=y+3 and y(0)=2, then y(log2) is equal to
Text Solution
|
Let I be the purchase value of an equipment and V(t) be the value afte...
Text Solution
|
Solution of the differential equation cosxdy=y(sinx-y)dx, 0ltxlt(pi)...
Text Solution
|
The differential equation which represents the family of curves y=c(1)...
Text Solution
|
The differential equation of the family of circles with fixed radius ...
Text Solution
|