Question

Please circle your final answer!

Question 13 Not yet answered Marked out of 10.00 Solve the following initial value problem. dy/dx + 3xy - 2x e^(-x) = 0 (first order linear DE) y(0) = 1000 Note that a b = ab. Flag question Select one: O a. y = (x2 + 1000)^{-x} O b. y = (x2 - 100)^{-x*} C. y =( X2 - 1000)^{-x*} d. y = (2x2 + 1000)^{-x}

Answer 1

equa tion is (13) Given n differential dy + 3x²y - zaé -x] die +3e'y xe x² dx = 2xe ولے x² T + 3x², y=zxé is in the The equation of form dy The t Peki ya QOX) which is linear ditterential equation with first order. , The integrating factor is I-F لے رحم ) e , 3x² dx = e 36x² ( لے e Jan de لے MAI tc ht!

3 (%) T-FE R) =e 3 ) .. 3 I. ت نع e Then the general soluation is y.(I'F) - 5 am). (T-F) dete (6x3, dx +C دیدم saxet علا 2 3 و د د 2 مر 2 e * dictc C ولا + رتر+له-) در2 = 2 ع detc 3 yet ع 7 = 2 = (e) ir + (.°=) 2 فور = 2 2/x dxto 3 2 محدود = 2 و + (ع) 2 - (اعد شده و ار tc

د yet = xt tc ای - 3 الحاد) ,ا کرم رہ کرے یا (2) To find's' Given initial condition ل = (م) و ههه Now equation o becomes -3 (x²tc - رع at kao 3 ره رہی ہے e e (۵)

eº=1 ri al 1000 = I (O+C) looo ICC) (200 C .. c=looo substitute Cralue in equation equation ③ becomes ya Now ex (² +1000)

"=(x²+1000) et Hence 3 y =(2²+1000) k which is required Soluation Note The option å is Correct answer