Question

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)

Answer #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

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.

Find all solutions to the differential equations.
(a) x^2 yy' = (y^2 − 1)^(3/2)
(b) y' = 6xe^(x−y)
(c) y' = (2x − 1)(y + 1)
(d) (y^2 − 1) dy/dx = 4xy^2
Leave your answer as an implicit solution

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)

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 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).

(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

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.

Consider the differential equation dy/dx= 2y(x+1)
a) sketch a slope field
b) Show that any point with initial condition x = –1 in the 2nd
quadrant creates a
relative minimum for its particular solution.
c)Find the particular solution y=f(x)) to the given differential
equation with
initial condition f(0) = 2
d)For the solution in part c), find lim x aproaches 0
f(x)-2/tan(x^2+2x)

(* Problem 3 *)
(* Consider differential equations of the form a(x) + b(x)dy
/dx=0 *) \
(* Use mathematica to determin if they are in Exact form or not.
If they are, use CountourPlot to graph the different solution
curves 3.a 3x^2+y + (x+3y^2)dy /dx=0 3.b cos(x) + sin(x) dy /dx=0
3.c y e^xy+ x e^xydy/dx=0

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