Giải phương trình vi phân a. dy/dx b. y’ + 2xy = 4x

Question

Giải phương trình vi phân
a. dy/dx
b. y’ + 2xy = 4x

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niczorrrr 5 months 2021-08-27T04:18:19+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-08-27T04:20:17+00:00

    Your first differential equation is incomplete, so I’ll just look at the second one.

    y’ + 2xy = 4x

    Multiply both sides by exp(x ²):

    exp(x ²) y’ + 2x exp(x ²) y = 4x exp(x ²)

    The left side is the derivative of a product:

    (exp(x ²) y ) = 4x exp(x ²)

    Integrate both sides:

    exp(x ²) y = ∫ 4x exp(x ²) dx

    For the integral, substitute u = x ² and du = 2x dx :

    exp(x ²) y = 2 ∫ exp(u) du

    Solve for y :

    exp(x ²) y = 2 exp(u) + C

    exp(x ²) y = 2 exp(x ²) + C

    y = 2 + C exp(-x ²)

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )