Let f: R- 1 R- 1 be a function satisfying the differential equation 2 x(y+x) d x-x^2(d x+d y)=(x+y)^2 d x with f(2)=2 . If area enclosed by y=f(x) and x -axis from x=2 to x=3 is (a+ b) where a, b N , then find the value of (a+b) .

Question

Quantrex Academy · Accepted Answer

Correct answer: 3

aligned & x^2 d y+y^2 d x=0 & d y y^2 + d x x^2 =0 -1 y - 1 x =C & (2,2) C=1 & 1 y + 1 x =1 y= x x-1 & Required area = ₂^3 x x-1 d x= ₂^3 (1+ 1 x-1 ) d x (x+ (x-1))₂^3=1+ 2 a+ b aligned Hence, a+b=3

Let f: R- 1 R- 1 be a function satisfying the differential equation 2 x(y+x) d x-x^2(d x+d y)=(x+y)^2 d x with f(2)=2 . If area enclosed by y=f(x) and x -axis from x=2 to x=3 is (a+ b) where a, b N , then find the value of (a+b) .

Correct answer

Step-by-step solution

More from Differential Equations