Question

solve all questions please

Question 1 The solution to the ODE y' + 3xy=0 is Question 2 The solution of the IVP Ý – 2y=e*, (0) = 2 is Question 3 The solution to the ODE Y'y=2-3y2 is Question 4 The solution to the ODE XY' – y=-xex

Answer 1

So the solution of equo is given by Y.C3-F-) = S(**) I f.). (a) da + c Here glade ex an to 7 y.e-2x Sentendent ex dut ㅋ y.e-2x = rend to T y.e-22 22 -e-de tce za y= 7 x tce za T -e ya when yco) = 2 -eo tc.ee 2 = 다. c = 3 의 y=-ext3e2x illya e My=ex ( 382-1)

3 y'ya - 2-342 7 dy (2-342) du y 여 dy =du (2-342) 의 y JG dy = = fante 2-342 substitute 2-3y=t 7-6ydy=dt 7 ydy a adt 6. ㅋ -Sat = xtc 7 -1 m(t) = x + c

ㅋ log (t) = - 6x + c' substitute za 2- 342 -6x+c - (2-342) - 7 Log ( 2-3y 2) = -buto 34 2 = ~) 2-c. eon (ec = c) 2. 2 7 y 2 -64 c e ایحا 3. ayla) = e-on) 5/50 (3-5cm) 3 3 .