Charity Marange
Dec 18, 2023
Define a linear differential equation?
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Dec 18, 2023
A linear differential equation is a differential equation in which the dependent variable and its derivatives appear only in a linear form. It can be written in the form:
a_n(x)y^n + a_{n-1}(x)y^{n-1} + ... + a_1(x)y' + a_0(x)y = g(x)
where y is the dependent variable, y' represents its derivative with respect to x, a_n(x), a_{n-1}(x), ..., a_1(x), a_0(x) are functions of x, and g(x) is a given function of x. The highest power of y and its derivatives in the equation is n, and the coefficients a_n(x), a_{n-1}(x), ..., a_1(x), a_0(x) can be constants or functions of x.
a_n(x)y^n + a_{n-1}(x)y^{n-1} + ... + a_1(x)y' + a_0(x)y = g(x)
where y is the dependent variable, y' represents its derivative with respect to x, a_n(x), a_{n-1}(x), ..., a_1(x), a_0(x) are functions of x, and g(x) is a given function of x. The highest power of y and its derivatives in the equation is n, and the coefficients a_n(x), a_{n-1}(x), ..., a_1(x), a_0(x) can be constants or functions of x.
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Gambuleni Phiri
Dec 18, 2023
What is computer
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