Question

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=

Answer #1

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)]

Find the solution of the Differential Equation
X^2y''-xy'+y=x

Verify that the indicated function is a solution of the given
differentialequation.x2y′′−xy′+ 2y= 0;y=xcos (lnx), x >0

1. Find the general solution to the differential equation y''+
xy' + x^2 y = 0 using power series techniques

Verify that the given function is the solution of the initial
value problem.
1. A) x^3y'''-3x^2y''+6xy'-6y= -(24/x) y(-1)=0 y'(-1)=0
y''(-1)=0
y=-6x-8x^2-3x^3+(1/x)
C) xy'''-y''-xy'+y^2= x^2 y(1)=2 y'(1)=5 y''(1)=-1
y=-x^2-2+2e^(x-1-e^-(x-1))+4x

a) Find the general solution of the differential equation
y''-2y'+y=0
b) Use the method of variation of parameters to find the general
solution of the differential equation y''-2y'+y=2e^t/t^3

Solve the Homogeneous differential equation
(7 y^2 + 1 xy)dx - 1 x^2 dy = 0
(a) A one-parameter family of solution of the equation is y(x)
=
(b) The particular solution of the equation subject to the
initial condition y(1) =1/7.

Find the differential Equation of
xy'-2y+(2x^3)e^-x=0

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

Let y be the solution of the equation
a)
y ′ = 2 x y, satisfying the condition y ( 0 ) = 1.
Find the value of the function f ( x ) = ln ( y ( x ) )
at the point x = 2.
b)
Let y be the solution of the equation
y ′ = sqrt(1 − y^2) satisfying the condition y ( 0 )
= 0.
Find the value of the function f ( x...

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