Question

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′= 0, y(0) = 1, y′(0) = 1.

Answer #1

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

Consider the differential equation. Find the solution y(0) =
2.
dy/dt = 4t/2yt^2 + 2t^2 + y + 1

Solve the following differential equation using Laplace dy/dt
+2y=12sin4t y(0) =10

consider the equation y*dx+(x^2y-x)dy=0. show that the equation
is not exact. find an integrating factor o the equation in the form
u=u(x). find the general solution of the equation.

Consider the autonomous differential equation dy/ dt = f(y) and
suppose that y1 is a critical point, i.e., f(y1) = 0.
Show that the constant equilibrium solution y = y1 is
asymptotically stable if f 0 (y1) < 0 and unstable if f 0 (y1)
> 0.

Consider the following differential equation: dy/dx =
−(3xy+y^2)/x^2+xy
(a) Rewrite this equation into the form M(x, y)dx + N(x, y)dy =
0. Determine if this equation is exact;
(b) Multiply x on both sides of the equation, is the new
equation exact?
(c) Solve the equation based on Part (a) and Part (b).

Write a matlab script file to solve the differential equation
dy/dt = 1 − y^3 with initial condition y(0)=0, from t=0 to t=10.
matlab question

dx/dt - 3(dy/dt) = -x+2
dx/dt + dy/dt = y+t
Solve the system by obtaining a high order linear differential
equation for the unknown function of x (t).

Solve the initial value problem 9(t+1) dy dt −6y=18t,
9(t+1)dydt−6y=18t, for t>−1 t>−1 with y(0)=14. y(0)=14. Find
the integrating factor, u(t)= u(t)= , and then find y(t)= y(t)=

Solve the differential equation (3y^2+2ty)+(2ty+t^2)dy/dt=0

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