AP EAMCET20225 Jul 2022Evening ShiftMathematicsDifferential EquationsActual
By multiplying with e^ P d x on both sides of the equation d y d x +P(x) y=Q(x) , the left side of the equation takes the form d d x (y f(x)) , then f(x)=
Options
- Ay e^ P d x d x
- By P(x)
- Ce^ P d x
- DP ( x ) e^ P d x
Correct answer
C. e^ P d x
Step-by-step solution
d y d x +P(x) y=Q(x) multiplying e^ P d x on both sides of eqn. e^ P d x d y d x +ye^ P d x P(x)=Q(x) e^ P d x equating LHS with d d x (y(f(x))) e^ P d x d y d x +y e^ P d x P(x)= d d x (y f(x)) d d x (y e^ P d x )= d d x y f(x)f(x)=e^ P d x