How do you do question b?

Question

asked Oct 10, 2021 19.3k views

1 Answer

Dynom · Answer 1 · 2021-10-15T20:36:36+0000

Part (b)

We use the result of part (a) and plug in (x,y) = (0,0). This is directly from the initial condition y(0) = 0.

$\arcsin(4y) = x^2 + C\\\\\arcsin(4*0) = (0)^2 + C\\\\\arcsin(0) = C\\\\0 = C\\\\C = 0\\\\$

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This means,

$\arcsin(4y) = x^2 + C\\\\\arcsin(4y) = x^2 + 0\\\\\arcsin(4y) = x^2\\\\4y = \sin(x^2)\\\\y = (1)/(4)\sin(x^2)\\\\$

is the solution with the initial condition y(0) = 0.