Question

The general solution to equation y" - 2y - 3y=0 is a. y=1e3! + ce- b. y=ce" + ce-1 C. y = c + c2e- d. none of the above

Answer 1

Note: ) Tx consider and onder linear differential equn with constant coefficients as, a, a, dy ay" +9y'+Qzy=0 Auxiliary equn of ") is given by a m²+a, mta=0 the auxiliary equn (2) of me, my are both real and distinct roots of (2) ; then general solum of (1) will by Y(*) (22 Let, my, me be two roots mza Gemix tee where el are arbitrary constants

soluna differential equn Y"-24"-3y=0 (0) Auxiliary equr of (1) is m²_am-3=0 m-3m tm-3=0 mm-3)+1( m-3)=0 =) (M-3) (m+1)=0 ㅋ m=3,-1 het, m,=3, Then general solun of I is arbitrary y = 90² te constants So, option @ 15 correct. m2 =-1 32 ; G.@ are