Home
Class 12
MATHS
A differentiable function y =g (x) satis...

A differentiable function `y =g (x)` satisfies `int _(0)^(x)(x-t+1)g (t) dt =x^(4)+x^(2),AAxge0.
`y =g (x)` satisfies the differential equation :

A

`(dy)/(dx) -y = 12 x^(2) +2`

B

`(dy)/(dx)+2y =12 x ^(2) +2`

C

`(dy)/(dx )+ y =12 x ^(2) +2`

D

`(dy)/(dx) +y =12x +2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|6 Videos

  • DIFFERENTIAL EQUATIONS

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|6 Videos

  • DETERMINANTS

    VK JAISWAL ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

  • ELLIPSE

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|2 Videos

Similar Questions

Explore conceptually related problems

A differentiable function y = g(x) satisfies int_0^x(x-t+1) g(t) dt=x^4+x^2 for all x>=0 then y=g(x) satisfies the differential equation

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int_(0)^(x)(x-t)f^(')(t)dt y satisfies the differential equation

If y(x) satisfies the differential equation y'-y tan x=2x and y(0)=0 , then

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . y=f(x) is

Let f :R ^(+) to R be a differentiable function with f (1)=3 and satisfying : int _(1) ^(xy) f(t) dt =y int_(1) ^(x) f (t) dt +x int_(1) ^(y) f (t) dt AA x, y in R^(+), then f (e) =

A differentiable function satisfies f(x) = int_(0)^(x) (f(t) cot t - cos(t - x))dt . Which of the following hold(s) good?

Let f be a differentiable function on R and satisfying the integral equation x int_(0)^(x)f(t)dt-int_(0)^(x)tf(x-t)dt=e^(x)-1 AA x in R . Then f(1) equals to ___

If f' is a differentiable function satisfying f(x)=int_(0)^(x)sqrt(1-f^(2)(t))dt+1/2 then the value of f(pi) is equal to

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

f:RrarrR be twice differentiable function satisfying f^(")(x)-5f^(')(x)+6f(x)ge0AAxge0 if f(0)=1 f^(')(0)=0 . If f(x) satisfies f(x),f(x)geae^(bx)-be^(ax), Aaxge0 , then find (a+b)