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

y' + 4x^3 * y = 4y^2 * e^4x * (1 - x^3) | y = 0 - частное решениеy'/y^2 + 4x^3 / y = 4e^4x * (1 - x^3) | z = 1/y, z' = -y'/y^2z*4x^3 - z' = 4e^4x * (1 - x^3)1.z*4x^3 - z' = 0z'/z = 4x^3ln|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) + C1z = C1 * e^(x^4) - e^4xy = 1 / (C1 * e^(x^4) - e^4x)