Consider the following differential equations: dy / dt = sin(3t - 1) dy / dt = 2

Question

Consider the following differential equations: dy / dt = sin(3t - 1) dy / dt = 2.1 dy / dt = 2ty + y / t dy / dx = x2 + 1 For each of the differential equations above, determine whether the differential equation is pure-time, autonomous, or neither. For each of the following functions, determine whether they arc solutions of any of the differential equations (1)-(4). y1(t) = tet + et y2(t) = t3 / 3 + 1 / t y3(t) = tet2 y4(t) = 2.1t - 3 y5(t) = 2.1 y6(t) = 2.1t y7(t) = cos(3t - 1) y8(t) = 1 + cos(3t - 1) / 3

Explanation / Answer

1) pure time= 1 may be 2 also autonomous=4 neither =3 2) solution of 1 can be none due to sign diff otherwie 12 solution of 2 can be 8,10 solution of 3 can be 7 solution of 4 can be none u can diff the solution to obtain the questn

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