Question

Using any method you prefer, find the IVP solution of the given probler y'' + 4y' = 0; y(0) = - 10, y'(0) = 36 The solution is y(t) =

Answer 1

Solutions y's 4y'=0 40)2-10 & 9') =36 » y + 4y =0 - 6%AD)y=0 fuciliary equation mam 20 m(m + 4) 20 mzo and m+420 m =-4 m2 0,-4

Y(0)2 – 46 e 4(0) Now, if equation is the form of it CF = cemat Gemet (-4) + e Colt ce 2 Ca e C.F. 2 C, + Get and also P. I = 0 general solution y (&)2 Cf & P.J. - 4t I g (t) z C + Cal if t zo -40 Y(0)2 C,& qe -10 C tę 6 -4t Now, differentiate eq@ with respect to 't' y (1) 2 çe X (-4) y (+)2 - 4 Gé -44 now put to

36 = 4 x L Ca 2 - 36 4 -9 Ga-9 now put the value of ca in eqı (b) G+q=-10 9-92-10 C,= 10+9 Ca E-l Now put the value of c, and a in eq (a) -4 t y(t) = Cat C y (4) z -I + (-9) e 4t y (t) = -|-gett Answer