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99 Percentile Qs Bank for JEE MainMathematicsDifferential Equations

The general solution of d y d x + y f^ ( x )-f( x ) f^ ( x )=0, y f(x) is

Options

  1. Ay =f( x )+1+ ce ^ -f( x )
  2. By=c e^ -f(x)
  3. Cy =f( x )-1+ ce ^ -f( x )
  4. Dy =f( x )+ ce f( x )

Correct answer

C. y =f( x )-1+ ce ^ -f( x )

Step-by-step solution

aligned & d y d x +y f^ (x)-f(x) f^ (x)=0 & d y d x +y f^ (x)=f(x) f^ (x) & P=f^ (x), Q=f(x) f^ (x) & I F=e^ P d x =e^ f^ (x) d x & I F=e^ f(x) & y I F= Q I F+C & y e^ f(x) = e^ f(x) f^ (x) f(x) d x & e^ f(x) =t & e^ f(x) f^ (x) d x=d t y e^ f(x) = t d t & y e^ f(x) =t t-t+C & y e^ f(x) =f(x) e^ f(x) -e^ f(x) +C & y=f(x)-1+C e^ -f(x) aligned

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