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

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)

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

Solve the Differential Equation:
(2y^4 + xy)dx - (6x^2) dy= 0

Solve the separable equation 3xy^2 dy/dx = x^2 + 1 given y(0)
=5
I am getting a general solution of cubed root
x2/2+ln|x|+3c1 when I enter the initial
conditions y(0)=5 the equation is undefined. How do deal with this?
What would the final answer be?
Thanks

Find the function whose derivative is given (i.e. solve each differential
equation). Note: E>G. Answers: A,B,D,E,F,G
a) dy/dx=6x^2. y(x)=Ax^B + C.
b) du/dt=8t(t^2 + 2). u(t)=Dt^E + Ft^G + C. ans:6

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