KCET2022MathematicsDifferential Equations
If d y d x + y x =x^2 , then 2 y(2)-y(1)=
Options
- A11 4
- B15 4
- C9 4
- D13 4
Correct answer
B. 15 4
Step-by-step solution
d y d x + y x =x^2 On comparing to d y d x +P(x) y=Q(x) aligned & P(x)= 1 x , Q(x)=x^2 & IF =e^ P d x =e^ 1 x d x =e^ x =x & y ( IF )= Q(x)( IF ) d x+C & y x= x^2 x d x+C= x^4 4 +C & y= x^3 4 + C x & y(2)= 2^3 4 + C 2 =2+ C 2 & y(1)= 1 4 + C 1 = 1 4 +C & 2 y(2)-y(1)=2 (2+ C 2 )- ( 1 4 +C ) &=4+C- 1 4 -C= 15 4 aligned