Homogeneous Equation. Please help me to solve exercise a, b and c

HOMOGENEOUS EQUATION Method of solution : step 1 : Replace day = > me , dy = > m and y = > I into the given dxo dx differential equation to form a characteristics equation- step a = find the roots of the characteristic equation - step 3 : In order to find the general solution of the differential equation , the type of root in step a is identified step 4 : The general solution of equation is obtained. step 5 : If there is an initial condition , then substitute the condition into the general solution to obtain the value of the unknown constant No : Subject:. Date : EXERCISE Determine the solution of the following differential equations . a ) yo - 6y' 1 9 4 = 0 Answer : y ( x ) = ( At B x ) e 3 x b ) 4 9 0 - 1 0 y' t qu = 0 , 4 10)= 0 and y'10 ) = -1 Answer = y (x ) = = (1- axle 3/2 x c ) H y " + 4 4 ' t y = 0, 4 10 ) = 2 and y' (12 = e's Answer : you ) = (4 x ta )esx