Question

1) Solve the given differential equation by separation of variables.

*e*^{x}* y*
dy/dx =

^{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(x^{2} + 1), x( π/4)= 1

Answer #1

Solve the given system of differential equations by systematic
elimination. 2 dx/dt − 6x + dy/dt = e^t
dx/dt − x + dy/dt = 6e^t

Consider the differential equation
x2 dy + y ( x + y) dx = 0 with the initial condition
y(1) = 1.
(2a) Determine the type of the differential equation. Explain
why?
(2b) Find the particular solution of the initial value problem.

Use the Laplace transform to solve the given system of
differential equations. 2 dx/dt + dy/dt − 2x = 1
dx/dt + dy/dt − 6x − 6y = 2
x(0) = 0, y(0) = 0

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

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.

Consider the differential equation y′′+ 9y′= 0.(
a) Let u=y′=dy/dt. Rewrite the differential equation as a
first-order differential equation in terms of the variables u.
Solve the first-order differential equation for u (using either
separation of variables or an integrating factor) and integrate u
to find y.
(b) Write out the auxiliary equation for the differential
equation and use the methods of Section 4.2/4.3 to find the general
solution.
(c) Find the solution to the initial value problem y′′+ 9y′=...

Solve the differential equation: dy/dx - y =e^x*y^2 (Using
u=y^-1)

(a) State the interval on which the solution to the differential
equation (x^2-1)dy/dx + ln(x+1)y = 4e^x
with initial condition y(2) = 4 exists. Do not attempt to solve the
equation.
ODE
SHOW ALL STEPS PLEASE.

differential equations solve
(2xy+6x)dx+(x^2+4y^3)dy, y(0)=1

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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