Substitute y(x)= 2 a,x" and the Maclaurin series for 6 sin 3x into y' - 2xy...
Substitute (x)=x" into " + xax' +2=x2 + 4x +9 and equate the coefficients of like powers of x on both sides of the equation to find the first four nonzero terms in a power series expansion about x-O of a general solution to the differential equation (Type an expression in terms of , and that includes all terms up to order 3.)
Substituto 2x x' into 2" + x2 +2+x? *** 3 and equate the coefficients of the powers of x on both sides of the equation to find the first four nonzero terms in a power series expersion about x = 0 of a general solution to the differential equation (Type an expression in terms of it, and a that includes al terms up to order 3.)
sin 3x 8. Find the first four nonzero terms in the Maclaurin series for f(x) = х 1 1 1 sin x = x - --- 203 + -25 120 X' +.. 5040 (14 pts.) 6
cnrn Consider the following differential equation. (1 + 3x?) y" – 2xy' – 12y = 0 (a) If you were to look for a power series solution about xo = 0, i.e., of the form Σ n=0 00 then the recurrence formula for the coefficients would be given by Ck+2 g(k) Ck, k > 2. Enter the function g(k) into the answer box below. (b) Find the solution to the above differential equation with initial conditions y(0) = 0 and...
The Maclaurin series for sin(x) is x + - + ... 3! 5! 7! sin You need not write your answer in summation notation, but you do need to list at least 4 nonzero terms. b) Find the Maclaurin series for xsin(x). You need not write your answer in summation notation, but you do need to list at least 4 nonzero terms. c) Use the first four terms of the appropriate power series to approximate V2 2
X 8.4.14 Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 4y' - 6 e 2xy = 0; y(0)=5 y(x)=+ (Type an expression that includes all terms up to order 3.)
8.3.11 Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. y' + (x + 4)y=0 +... y(x)=+. (Type an expression in terms of a, that includes all terms up to order 3.)
8.3.14 Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. (x2 + 4) y'' +y=0 + ... y(x) = (Type an expression in terms of a, and a that includes all terms up to order 3.)
Find at least the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. y'' + (x + 4)y' + y = 0 yax=20 (1-**3) +a,(x-26?- ***) - X (Type an expression in terms of a, and a, that includes all terms up to order 3.)
X 8.4.14 Question Help Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem 6y' - 4 e 2xy = 0; y(0)=5 y(x) = (Type an expression that includes all terms up to order 3.)