Question

The general solution of the DE ` (dy)/(dx) + (y)/(x) = x ^(2) ` is
A. `xy = x ^(4) + C `
B. `4xy = x ^(4) + C `
C. ` 3xy = x ^(3) + C `
D. none of these

Answer 1

Correct Answer - B
Given DE is linear.
`IF = e ( int (1)/(x) dx ) = e (log x ) = x `
` therefore y xx x = int ( x xx x ^(2)) dx = int x ^(3) dx = (x ^(4))/( 4) + C `
` rArr 4xy = x ^(4) +C`.