EXERCISE 10.4

EXERCISE . . Show that each of the following expressions is a solution of the corresponding given differential equation. (i) = ; xy ' = (ii) ae be ; ′′− . Find value of m so that the function y e mx is a solution of the given differential equation. (i) ' + (ii) y '' ' . The slope of the tangent to the curve at any point is the reciprocal of four times the ordinate at that point. The curve passes through ( , ). Find the equation of the curve. . Show that y mx is a solution of the differential equation e d y  −= . Show that y ax x x ≠ is a solution of the differential equation x y ′′+ ′− . Show that y ae − , where a and b are arbitrary constants, is a solution of the differential equation d y . Show that the differential equation representing the family of curves y a x     , where a is a positive parameter, is y xy dy y dy  =    . . Show that y bx is a solution of the differential equation d y b y Now, we discuss some standard methods of solving certain type of differential equations of the first order and first degree.