554 Ordinary Differential Equations- a. qp(t) =EC b. EC c. 0
- a. ip(t) = E(l - eRt/L)jR , limt_,+ooip(t) = E/R
b. ip(t) = E(Lw sinwt + Rcoswt)/(R^2 + (Lw)^2 )
Exercises 6.2 Higher Order Differential Equations
l. a. Y1 = c 1 cos(2.07302t) + c2 sin(2.07302t) + c3 cos(9.56122t)
+c 4 sin(9.56122t)b. Y2 = l.3764107c1 cos(2.07302t) + l.3764107c2sin(2.0 7302t)
- .2075804c3 cos(9.56122t) - .2075804c 4 sin(9.56122t)
C. C1 = - .0815925,
C4 = .0008474028C2 = .140808, C3 = .18 15925 ,
3. Y1 = .0567167 cos(3.94038t) + .0 184145 sin(3.94038t)
-.0067167 cos(9.08148t) + .0085272 sin(9.08148t)Y2 = .0743975 cos(3.94038t) + .024 1549 sin(3.94038t)
+ .0256022 cos(9.08148t) - .0325033 sin(9.08148t)- Yi = c 1 e-.366290t + c 2 e-4.84005t + c 3 e-15.7937t + u
Y2 = l.211237c 1 e-·^366290 t - .2666667c 2 e -^4 ·^84005 t - 3.666667c 3 e-^15 ·^7937 t
+u
y3 = l.278117c 1 e-·^366290 t - .9074786c 2 e-^4 ·^84005 t + 2.388889c 3 e-^15 ·^7937 t
+u- y = c 1 e·^387298 xcos(.387298x) + c2e·^387298 xsin(.387298x)
+ c 3 e-·^387298 x cos( .387298x) + c 4 e-·^387298 x sin( .38 7298 x)woL^4 cos( ?rx / L)
+ E!?r^2 (7r^2 - .09L2)