Question

P. 230 General Solution differential equation (Ist order) Y'tity=cost+too

Answer 1

Que. P.23. Solution Griven differential equation is, y' + y = cost i to O

- compaining equation ① with y't Py =d po 1 , then integrating factor (1.F.) = ef Pdt -Sat we get Cont е If e (using P-1) -t е + c t y e Copt dt to -t e Now, I = Then general solution of equation 0 y (I.F.) s (I.F.)« Q dt where 'c' is arbitroroy constant. ie. set cont dt I +C, where I = J et cont dt © set cont at et sint fint - s tét) sint dt et sint & S et sint at Rint + [ē tecost) – 5 -ētfCont) dt7 = et et sint et cost Set cost at ēt (eint -- cont) (sint - Cont) é t(sint - Copt) I = - e t 11 e I I 11 t 2 I = e :-) =) I - 2 Uning above volene of I in equation @ we get,

yet t (Rint-Cost) +C 11 2 :-) y = sint -cost tc. et 2 which is the required solution of given diferential equation.