Question

Consider the following group of differential equations

y´+y=F(x), where

F(x)= x^{2}, x^{3},...,x^{n}

F(x)= sen x

F(x)= [x]

Resolve taking into account the above:

a. Find the solution for each of the differential equations

b. Discuss the trend approach between y (x) and f (x)

c. Describe characteristics of the pattern that constitutes the expression of the solution y (x) and discuss it in the light of any known method

Please help me to solve!

Answer #1

Let X = ( X1, X2, X3, ,,,, Xn ) is iid,
f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b
< 1
then,
Show the density of the statistic T = X(n) is given by
FX(n) (x) = n/ab * (x/a)^{n/(b-1}} for 0 <= x <=
a ; otherwise zero.
# using the following
P (X(n) < x ) = P (X1 < x, X2 < x, ,,,,,,,,, Xn < x
),
Then assume...

1- Solve the following differential equations:
a) y ' = y / (x (lnx))
b) (eˆ (-y)) * (y '+ 1) = x (eˆx)
c) x '- (tan (t)) * x = sen (t)
d) y '= 1-y + (eˆ (2x)) * (yˆ2)

QUESTION 2
Consider the differential equation:
x2 y'' - 4 x y' + 6 y = 4 x3
If yc= c1 x2 + c2
x3, then yp(1) equals
(enter only a number; yp(1) is the particular
solution for the differential equation, evaluated at 1)

Consider differential equation: x3
(x2-1)2 (x2+1) y'' + (x-1) x y' +
y = 0 .. Determine whether x=0 is a regular singular
point. Determine whether x=1 is a regular singular point.
Are there any regular singular points that are complex numbers?
Justify conclusions.

Use the method for solving Bernoulli equations to solve the
following differential equation.
(dy/dx)+4y=( (e^(x))*(y^(-2)) )
Ignoring lost solutions, if any, the general solution y=
______(answer)__________
(Type an expression using x as the variable)
THIS PROBLEM IS A DIFFERENTIAL EQUATIONS PROBLEM. Only people
proficient in differential equations should attempt to solve.
Please write clearly and legibly. I must be able to CLEARLY read
your solution and final answer. CIRCLE YOUR FINAL ANSWER.

Given the following equations
y´(x)+y(x)=e-x; 2y´(x)+y(x)=e-x ;
y´(x)+2y(x)=e-x
a. Use the integration factor and find your
solutions
b. Discuss the trend behavior of the solutions and (x) as
follows:
1. compare the graphs of y (x) with the graphs of F (x)
2. Compare the graphs of y (x) with respect to the coefficients of
the differential equations

Consider the following system of linear equations:
2x1−2x2+4x3
=
−10
x1+x2−2x3
=
5
−2x1+x3
=
−2
Let A be the coefficient matrix and X the solution matrix to the
system. Solve the system by first computing A−1 and then
using it to find X.
You can resize a matrix (when appropriate) by clicking and dragging
the bottom-right corner of the matrix.

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

Exercise 178 Further problems on equations of the form dy
dx=f(x). In Problems 1 to 5, solve the differential
equations.
1.dy/ dx = cos4x−2x
2. 2xdy/dx =3−x3
3.dy/dx +x=3, given y=2 when x=1
4. 3d/ dθ +sin θ=0, given y=2/3when θ=π 3
5.1/ex +2=x−3dy/dxgiveny= y=1 when x=0.
6. The gradient of a curve is given by: dy dx + x2 2 =3x
engineering mathematics

solve the following system of differential equations
and find the general solution
(D+3)x+(D-1)y=0 and 2x+(D-3)y=0
please show the steps

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