Question

3. Find the general solution to the differential equation:

(x^2 + 1/( x + y) + y cos(xy)) dx + (y ^2 + 1 / (x + y) + x cos(xy)) dy = 0

Answer #1

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

Find the general solution of the given differential equation
(x+!) dy/dx + (x+2)y = 2xe^-x
y = ______
Determine whether there are any transient terms in the general
solution.

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

Find the General Solution of the Differential Equation (y' =
dy/dx) of
xy' = 6y+9x5*y2/3
I understand this is done with Bernoullis Equation but I can't seem
to algebraically understand this.

Find the general solution to the differential equation: y’’ – 6
y’ + 13y = 0
Find the general solution to the differential equation: y’’ +
5y’ + 4y = x + cos(x)

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.

1- Find the solution of the following equations. For each
equation, 2- determine the type of the category that the equation
belongs to.
1. y/x cos y/x dx − ( x/y sin y/x + cos y/x ) dy = 0
2. x(1 − y^2 )dx + y(8 − x^2 )dy = 0
3. (x^2 − x + y^2 )dx − (e^y − 2xy)dy = 0
4. 2x sin 3ydx + 3x^2 cos 3ydy = 0
5. (x ln x −...

Question 11:
What is the general solution of the following homogeneous
second-order differential equation?
d^2y/dx^2 + 10 dy/dx + 25.y =0
(a)
y = e 12.5.x (Ax + B)
(b)
y = e -5.x (Ax + B)
(c)
y = e -10.x (Ax + B)
(d)
y = e +5.x (Ax + B)
Question 12:
What is the general solution of the following homogeneous
second-order differential equation?
Non-integers are expressed to one decimal place.
d^2y/dx^2 − 38.y =0
(a)
y...

3. Consider the differential equation: x dy/dx = y^2 − y
(a) Find all solutions to the differential equation.
(b) Find the solution that contains the point (−1,1)
(c) Find the solution that contains the point (−2,0)
(d) Find the solution that contains the point (1/2,1/2)
(e) Find the solution that contains the point (2,1/4)

find the solution of the first order differential equation
(e^x+y + ye^y)dx +(xe^y - 1)dy =0 with initial value y(0)= -1

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