حل سؤال 19 %7VOH.W.pdfErereises.Solve the following differential equations:(1) "-- by =0(2) "+ 2y =0(3) " + 2y +y =0(4) " + 9y = 0(5) " - G/ + 13y = 0(6) " - 4 + 5y = 0(7) "- 4y + 4y = 0(8) " + 6y + 10y = 0(9) " + -0(10) "+ 6y + 13y = 0(11) 10y" - 3y -y=0(12) 4" + 4y + 10y =0Solve the initial value problems:(13) y" - 4y +3y = 0; y(0) - -1, / (0) = 3(14) y" + 4y= 0; y() 1, () = -4(15) 6y" - - y = 0; y(0) = 10, g'(0) = 013(16) 4" - 4y - 3y- 0; v(0) =12(0) -(17) y"+ 7y' + 12y = 0; y(0) = -1,(0) = 0(18) 36y" – 12y + y = 0; y(0) = 3, (0) =(19)(a) Suppsoe that y is a solution of the differential equationay" + by + cy = 0.Let :(r) - s(r - ro) where ro is an arbitrary real number. Show thata:" + be' + es =0(b) Let z1(a) = yn(r- ro) and z2(x) = 2(r - ro), where yG = CI1 + caa is the general solution to ay" +by +cy = 0. Show that se = e +gz is also a general solution of ay" + by/ + cy =0.

Name: حل سؤال 19 %7VOH.W.pdfErereises.Solve the following differential equat
Uploaded: 2024-03-20T07:06:41.000Z
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Description: حل سؤال 19 %7VOH.W.pdfErereises.Solve the following differential equations:(1) "-- by =0(2) "+ 2y =0(3) " + 2y +y =0(4) " + 9y = 0(5) " - G/ + 13y = 0(6) " - 4 + 5y = 0(7) "- 4y + 4y = 0(8) " + 6y + 10y = 0(9) " + -0(10) "+ 6y + 13y = 0(11) 10y" - 3y