Verify that the given family of functions solves the differential equation. (i)
dy dt
(ii)
dy dt
= (1 − 2t)y2, y = (c) Evaluate the integral
= y2 sin t, y = 1
0 ( 1
C − t + t2 . 1
C + cos t x2
√ . 4 − x2)3 dx
1
Expert's answer
2020-06-29T17:12:44-0400
(i) Given dtdy=(1−2t)y2 and y=c−t+t21
Differentiating y with respect to x,
dxdy=−(c−t+t21)2(−1+2t)=(c−t+t21)2(1−2t)
replacing value of y
we obtain, dtdy=(1−2t)y2
(ii) Given dtdy=y2sin(t) and y=c+cost1
differentiating both sides with respect to x,
dtdy=−(c+cost1)2(−sint)=(c+cost1)2(sint)
replacing value of y with y
we obtain, dtdy=y2sin(t)
(iii) We need to find integration of ∫01x2(4−x2)3dx
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