Question

a.) Solve the following IVP. X !=3x,-13x2 X, (O)=3 X2 = 5x +X2 X₂(0)=-10 b.) solve the following IVP. X;= -X, +(3/2) X2 X, (2)=1 X 2 = (-%6) xx-2x2 X2 (2)=0

Answer 1

We put value of c. 4 cm get X,2 e 2t (3 cas et + 133 sinat) X22 [ 02 + ( 3 Cas&+ + 133 sin® +) - 8e2* (-3 s'y 6+ + 133 cas8t)]

1.4 ct 1.54 C2 - 3.287 C, -2.9025 C2 + 2.17oc, & 1.935 C2 Oz .3 11c, & 0.5725 G solving equation e a we get c & C2 Ciz 17.75 -9.64 Xiz Zt (۱۶۰ 7.45 cash + 7, cụ » 53) X2 = le sinh. 9.64 Cash & 22 T2 2 t e - the 17.95 cash + 4. ck SĨA ++) t (11.rs cash t - 9.64 Sinh t)] ezt +