Question

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.

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

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

Solve the given differential equation
y-x(dy/dx)=3-2x2(dy/dx)

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 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.

1) Solve the given differential equation by separation of
variables.
exy
dy/dx = e−y +
e−6x −
y
2) Solve the given differential
equation by separation of variables.
y ln(x) dx/dy = (y+1/x)^2
3) Find an explicit solution of the given initial-value
problem.
dx/dt = 7(x2 + 1), x( π/4)= 1

Find the solution of the following differential
equation:
(?^3 y/dx^3)-7(d^2 y/dx^2)+10(dy/dx)=e^2x sinx

Solve the differential equation (5x^4 y^2+ 2xe^y - 2x cos (x^2)) dx
+ (2x^5y + x^2 e^y) dy = 0.

The differential equation given as dy / dx = y(x^3) -
1.4y, y (0) = 1 is calculated by taking the current h = 0.2 at the
point x = 0.6 and calculated by the Runge-Kutta method from the 4th
degree, find the relative error.
analytical solution: y(x)=e^(0.25(x^4)-1.4x)

Find the solution to the separable differential equation dy =
x cos2 y + sin x cos2 y satisfying π dx
the initial condition y = 4 when x = π.

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