Question

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.

Answer #1

(1 point) Solve the separable differential equation
?′(?)=√(4y(x)+32), and find the particular solution satisfying the
initial condition ?(1)=−4. ?(?)=__________.

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 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.

Find the solution for the differential equation
( 4tan(4x) − 4sin(4x) sin(y) ) dx + ( cos(4x) cos(y) ) dy = 0
Has solutions of form F( x, y ) = c ,where
F ( x ,y ) = ?
Please show your work step by step, thanks.

dx
+ (x cot y + sin y) dy=0, Solve the differential equation and write
your answer without negative exponents.

(b) Solve the separable differential
equation
y'=
(7e^-3x+2x^2-xcosx)/-6y^3
(c) Solve the IVP
x(1-siny)dy=(cosx-cosy-y)dx
.
y(π/2)=0

Use
a slope field plotter to plot the slope field for the differential
equation
dy/dx=sqrt(x-y)
and plot the solution curve for the initial condition
y(2)=2

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)

(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

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.

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