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Which of the following is the solution of the initial value problem y (5) + 4y (4) + 4y (3) = 0 , y(0)= 0 , y0 (0)= − 1 2 , y(2)(0)= 5 , y(3)(0)=−14 , y (4)(0)= 36 ? (a) y = −1 − t 4 + t 2 2 + e −2t (b) y = 1 4 − t + t 2 4 − 1 4 e −2t − te−2t (c) y = − 1 4 + t + 1 4 e −2t − te−2t (d) y = −1 + t 2 − t 2 4 + (1 + t 2 )e 2t (e) y = 1 2 + t − 1 2 e 2t + t 2 e 2t
Which of the following is the appropriate form for a particular solution of the differential equation y (4) + 3y 00 − 4y = 2x + cos2 x − cosh x ? (a) yp = (A + Bx)e x + (C + Dx) cos(2x) + (E + F x) sin(2x) (b) yp = (Ax + B)e −x + (C + Dx) cos(−x) + (E + F x) sin(−x) (c) yp = Ax + Bx2 + (C + Dx) cos x + (E + F x) sin(−x) + Ge2x (d) yp = Ax + Bx2 + (C + Dx) cos(2x) + (E + F x) sin(−2x) + Ge−x (e) yp = A + Bx + Cx sin(−2x) + Dx cos(2x) + Exex + F xe−x
Solve the partial differential equation (3D^² +10DD^1+ 3D ^1^2)z=e^x-y
Solve
(D^(2)-DD'-2D'^(2)+2D+2D')z=sin(2x+y)
Solve
(D^(2)+DD'-6D'^(2))z=y cosx
orthogonal trajectories of y' = - (x/y)
F or the follow ing differential equation locate and classify its singular points on the x-axis
𝑥
2
𝑦
′′ + (2 − 𝑥 )𝑦
′ = 0.
S how that y = c 1
e
x + c 2
e
2 x
is the general solution of y
′′ − 3 y
′ + 2y = 0 on any
interval, and find the particular solution for w hich y 0 = − 1 a n d y
′
( 0) = 1.
Solve the initial value problem (IVP):
(D^2+4D+4)=9e^x
y(0)=2
y'(0)=1
Solve the partial differential equation (3D² +10DD'+ 3D ^1^2)z^ =e^x-y
