Question

Solve the given initial-value problem. (Enter the first three nonzero terms of the solution.)

(* x* + 2)

Answer #1

Find the first five nonzero terms in the solution of the given
initial value problem.
y′′−xy′−y=0, y(0)=5, y′(0)=8
Enter an exact answer.

Find the first five nonzero terms in the solution of the given
initial value problem.
y′′+xy′+2y=0, y(0)=5, y′(0)=9
Differential Equations

7. Determine
the first 4 nonzero terms of the Taylor series for the solution
y = φ(x) of the given initial value
problem, y’’ +
cos(x)y’ +
x2y = 0; y(0) = 1,
y’(0) = 1.
What do you expect the radius of convergence to be? Why?
please show all steps

Find the first four nonzero terms in a power series expansion
about x=0 for the solution to the given initial value problem.
w''+3xw'-w=0; w(0)=8, w'(0)=0

Find first three nonzero terms, or as many as exist, in the
series expansion about x=0 for general solution to the given
equation for x>0. 5x(x-1)y''+9(x-1)y'-y=0.

Find the power series solution around x=0. Find the first few
nonzero terms of each solution. Power series are not necessary to
solve try older methods in addition to power series.
1) y”+x^2y=0

Use the power series method to find the solution of the initial
value problem. Write the first eight nonzero terms of the power
series centered at x = 0.
y′′= e^y, y(0) = 0, y′(0) = −1

Solve the given initial value problem and determine at least
approximately where the solution is valid.
(12x2+y−1)dx−(18y−x)dy=0, y(1)=0
y= ,
the solution is valid as long
as ≥0

Find the first four nonzero terms in the Taylor series expansion
of the solution of (x 2−2x)y 00+2y = 0, y(1) = −1, y 0 (1) = 3
about x0 = 1.

Solve the given initial-value problem in which the input
function g(x) is discontinuous. [Hint:
Solve the problem on two intervals, and then find a solution so
that y and y' are continuous at
x = π/2.]
y'' + 4y = g(x), y(0) = 1, y'(0) =
3, where
g(x) =
sin(x),
0 ≤ x ≤ π/2
0,
x > π/2
Find y(x) for each of the intervals.
,
0 ≤ x ≤ π/2
,
x > π/2

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