Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2024MathematicsDifferential Equations

The solution of e^ d y / d x =x+1, y(0)=3 is

Options

  1. Ay-2=x x-x
  2. By-x-3=x x
  3. Cy-x-3=(x+1) (x+1)
  4. Dy+x-3=(x+1) (x+1)

Correct answer

D. y+x-3=(x+1) (x+1)

Step-by-step solution

e^ d y d x =x+1 d y d x = (x+1) d y= (x+1) d x y=x (x+1)- x x+1 d x y=x (x+1)- 1 d x+ 1 1+x d x y=x (x+1)-x+ (x+1)+C y=(x+1) (x+1)-x+C Now, y(0)=33=0+C C=3 Hence, y=(x+1) (x+1)-x+3y+x-3=(x+1) (x+1)

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

The general solution of the differential equation (x y x ) d y= (y y x -x ) d x is 2025The general solution of the differential equation (x+y) d y=d x is 2025If Ax ^3+ Bxy =4 (A and B are arbitrary constants) is the general solution of the differential equation F(x) d^2 y d x^2 +G(x) d y d x -2 y=0 , then F(1)+G(1)= 2025If y=A t^2+ B t (A,B are parameters) is general solution of the differential equation f(t) y^ (t)+g(t) y^ (t)+h(t) y=0 then 2 f(t)+t^2 h(t)= 2025The general solution of the differential equation (2 x-y)^2 d y-2(2 x-y)^2 d x-2 d x=0 is 2025The general solution of the differential equation x x d y=(x x-y) d x is 2025If a and b are arbitrary constants, then the differential equation corresponding to the family of curves y= (a x+b) is 2025The general solution of the differential equation x y(y+2) d y+ (y^3-1 ) d x=0 is 2025 Full Differential Equations list All KCET PYQs