Question

Verify that the equation y = x^{2}+ 2x+2+Ce^{x}
is a solution to the differential equation
y'-y+x^{2}=0.

Answer #1

Verify that y=x2 ln(x), is a solution of the
differential equation x2y''-2y=3x2

differential equation(2x+3y)dx+ (y+2)dy=0

Verify that the function
y=x^2+c/x^2
is a solution of the differential equation
xy′+2y=4x^2, (x>0).
b) Find the value of c for which the solution satisfies the initial
condition y(4)=3.
c=

Verify that the given functions form a fundamental set of
solutions of the differential equation on the indicated interval.
Form the general solution.
1.) y'' − 4y = 0; cosh 2x, sinh 2x, (−∞,∞)
2.) y^(4) + y'' = 0; 1, x, cos x, sin x (−∞,∞)

Consider the differential equation x2y''+xy'-y=0,
x>0.
a. Verify that y(x)=x is a solution.
b. Find a second linearly independent solution using the method
of reduction of order. [Please use y2(x) =
v(x)y1(x)]

Verify that all members of the family y =
(2)1/2 (c -
x2)-1/2 are solutions of the
differential equation
Find a solution of the initial-value problem. y' = (xy^3)/2 ,
y(0) = 9

Consider the differential equation
4x2y′′ − 8x2y′ + (4x2 + 1)y = 0
(a) Verify that x0 = 0 is a regular singular point of the
differential equation and then find one solution as a Frobenius
series centered at x0 = 0. The indicial equation has a single root
with multiplicity two. Therefore the differential equation has only
one Frobenius series solution. Write your solution in terms of
familiar elementary functions.
(b) Use Reduction of Order to find a second...

Consider the differential equation y' = x − y + 1:
(a) Verify that y = x + e^(1−x) is a solution to the above
differential equation satisfying y(1) = 2;
(b) Is the solution through (1, 2) unique? Justify your answer
in a few sentences;
(c) Is this differential equation separable? Find the general
solution of y' = x − y + 1.

given the differential equation y'+y=x^2+2x, compute the value of
the solution y(x) at x=1 given the inital condition y(0)=2. Also,
use h=0.1

Show that f(x) = C1e4x +
C2e-2x is a solution to the differential
equation: y’’ – 2y’ – 8y = 0, for all constants C1 and
C2. Then find values for C1 and C2
such that y(0) = 1 and y’(0) = 0.

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