Substitute y(x)= 2 a, x" and the Maclaurin series for 6 sin 3x into y' - 2xy = 6 sin 3x and equate the coefficients of like powers of x on both sides of the equation to n= 0 find the first four nonzero terms in a power series expansion about x = 0 of a general solution to the differential equation. У(х) = +.
(Type an expression in terms of a, that includes all terms up to order 6.)

Substitute and the Maclaurin series for 6 sin 3x into y' - 2xy = 6 sin 3x and equate the coefficients of like powers of x on both sides of the equation to n= 0 find the first four nonzero terms in a power series expansion about x = 0 of a general solution to the differential equation.

У(х) = ____ +.

(Type an expression in terms of a, that includes all terms up to order 6.)

Step-by-step explanation:

Relating the coefficient of constant term

Relating the coefficient of x¹

Relating the coefficient of x²

Relating the coefficient of x³

where;  

Divide both sides by 4

Relating coefficient of x⁴

Relating coefficient of x⁵

Divide both sides by 2

where;

Divide both sides by 3

Thus:

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.

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