Решить дифференциальное уравнение: [latex] y'+4x^{3} y=4y^{2} e^{4x} (1- x^{3} ) [/latex]

y' + 4x^3 * y = 4y^2 * e^4x * (1 - x^3) | y = 0 - частное решение y'/y^2 + 4x^3 / y = 4e^4x * (1 - x^3) | z = 1/y, z' = -y'/y^2 z*4x^3 - z' = 4e^4x * (1 - x^3) 1. z*4x^3 - z' = 0 z'/z = 4x^3 ln|z| = x^4 + ln|C| | C = C(x) z = C * e^(x^4) z' = C * 4x^3 * e^(x^4) + C' * e^(x^4) 2. C * e^(x^4) * 4x^3 - C * 4x^3 * e^(x^4) - C' * e^(x^4) = 4e^4x * (1 - x^3) C' = -4e^(4x - x^4) * (1 - x^3) C = -e^(4x - x^4) + C1 z = C1 * e^(x^4) - e^4x y = 1 / (C1 * e^(x^4) - e^4x)