Question

Solve the following Bernoulli equations:

1) (2+x^2)y' +xy=x^3y^3

2) y′(x) + y/(x-2) = 5(x − 2)y^(1/2)

Answer #1

1.

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= ?

Solve the following:
(3x^2 - y^2)dx + (xy - x^3y^-1)dy = 0

Solve the following non-linear differential equations.
y'=xy''-x(y')^2

Solve the following differential equations through order
reduction.
(a) xy′y′′−3ln(x)((y′)2−1)=0.
(b) y′′−2ln(1−x)y′=x.

1. solve the system of equations:
x+3y=9
3x+9y=27
please solve to get the x and y solution
2. solve the system of equations, please state the x and y
solution
9x-4y=23
15x+4y=41
3. solve the system of equations please state the x and y
solution
x - y - z = 1
5x + 6y + z = 1
30x + 25y = 0

Solve the following nonhomogenous Cauchy-Euler equations for x
> 0.
a. x^(2)y′′+3xy′−3y=3x^(2).

Solve the equation.
(2x^3+xy)dx+(x^3y^3-x^2)dy=0
give answer in form F(x,y)=c

Use Scilab to solve the following set of nonlinear algebraic
equations: x^3y -4y^2 +3x = 1 and 6y^2 - 9xy= 5 with initial
guesses of x = 2, y = 2.

Solve the following Bernoulli equation.
(x^2)y' + 4xy = 9^3
Answer: y = +/- (_______)

Solve the following system of equations simultaneously. Give
answers for both x and y.
2x-5y=1
x+3y=6

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