Question

about y' = x-y, y(0) = 0,

(1) find solution

(2) use direction field draw approximation solution on xy plane and compare with the result (1)

Answer 1

solution 1 [Page-t] Griven ODE with initial Condition : y = x-y, 700)=0-) 7 ay [linear Equation of Now, solving equ- (2) first order] we get, of the form ay + y = x dy & Py = al Her Pan UR Therefore, The Integrating factor IF = Spax - e de et From equ. (2) - Multiplying both sides of Equ ) we get, by f. f = 1² | 7 + = ? 7 a lety) = xeda Integrating both sides we get, y = [relax & C [co constant y = ²(x-1) + c y = (x-1) + cex-3) sides by ea] [ Dividing both

Now, Page-2] using Initial condition, y (0) = 0 from Equ. 3), we have. yo) = (0-1) + C. eo 7 col=0 Therefore solution is , The particular y = (x-1 & ex Here, We draw a graph of this solution :- 10 + y = (2-1) te 2 trx -5 0 5 10 15 20

اااااااا slope - Field :- کیا م عنی ہے oاور

Slope - Field - - ( y'= x+y

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