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find y in terms of x?
given that d^2y/dx^2=4 and when x=0 , y=2 and dy/dx=8, find y in terms of x
2 Answers
- cidyahLv 77 years ago
d^2y /dx^2 = 4
Integrate both sides
dy/dx = 4x+C
when x=0, dy/dx = 8
8 = 4(0) + C
C = 8
dy/dx = 4x+8
Integrate both sides
y = 4 (x^2 /2) + 8x + C
y = 2x^2 + 8x+ C
when x=0, y=2
2 = 2(0)^2 + 8(0) + C
C = 2
y = 2x^2 + 8x+ 2
- 7 years ago
y = ⌡⌡d^2y/dx^2 =⌡ dy/dx = ⌡⌡4 = ⌡4x + C = 2x^2 + Cx +K
dy/dx|(x=0) = 8 = 0 + C ==> C = 8
d^2y/dx^2|(x=0) = 2 = 0 + 0 + K ==> K = 2
y = 2x^2 + 8x + 2
