Question

dy/dx=4x³+4sin x is equal to

Answer 1

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♦ First-Order Seperable ODE ♦

→  y' = 4x³ + 4( sin x )

→ Integrating both sides, w.r.t.x :
  • [tex] \int\limits {y'} \, dx = \int\limits {4x^3 + 4sin x} \, dx \\ \\ =\ \textgreater \ y + c_1 = \int\limits {4x^3} \, dx + \int\limits {4sinx} \, dx \\ \\ =\ \textgreater \ y + c_1 = x^4 - 4 cos x + c_2 \\ \\ =\ \textgreater \ y = x^4 - 4cosx + C[/tex]

=> y( x ) = x⁴ - 4( cos x ) + C
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♥ Hope this helps ^_^