Question

Consider the differential equation x′=[2 −2 4 −2], with x(0)=[1 1] Solve the differential equation wherex=[x(t)y(t)]

please write as neat as possible better if typed and explain clearly with step by step work

Answer #1

solve the given differential equation (x^2) y’’ -6y=0
please explain step by step

Solve the differential equation with initial value
y''−2y'+y=e^t/(1+t^2), y(0) = 1, y'(0) = 0.

solve differential equation ((x)2 - xy +(y)2)dx - xydy
= 0
solve differential equation (x^2-xy+y^2)dx - xydy =
0

Consider the differential equation t 2 y" + 3ty' + y = 0, t >
0. (a) Check that y1(t) = t −1 is a solution to this equation. (b)
Find another solution y2(t) such that y1(t) and y2(t) are linearly
independent (that is, y1(t) and y2(t) form a fundamental set of
solutions for the differential equation)

Consider the differential equation x^2 y' '+ x^2 y' + (x-2)y =
0
a) Show that x = 0 is a regular singular point for the
equation.
b) For a series solution of the form y = ∑∞ n=0 an
x^(n+r) a0 ̸= 0 of the differential equation about
x = 0, find a recurrence relation that defines the coefficients
an’s corresponding to the larger root of the indicial equation. Do
not solve the recurrence relation.

Solve the differential equation:
a) y'= t^2y^3 / t^3+6
b) y'= x(e^x^2 +2) / 6y^2 ; y(0) =1

Consider the following differential equation:
dydx=x+y
With initial condition: y = 1 when x = 0
Using the Euler forward method, solve this differential
equation for the range x = 0 to x = 0.5 in increments (step) of
0.1
Check that the theoretical solution is y(x) = - x -1 , Find the
error between the theoretical solution and the solution given by
Euler method at x = 0.1 and x = 0.5 , correct to three decimal
places

Solve the differential equation
y^' − xy = e^x y(0) = 2

Solve the differential equation y'+(4/x) y=x^3 y^2

Solve the following differential equation using the power series
method. (1+x^2)y''-y'+y=0

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