Question

Find a solution of x dy dx = y2 − y that passes through the indicated points. (a) (0, 1) y =

(b) (0, 0) y =

(c) 1/ 3 , 1 /3 y =

(d) 2, 1/ 8 y =

Answer #1

1.Solve the following initial value problem
a) dy/dx= y2/(x-3), with y(4)=2
b) (sqrt(x)) dy/dx = ey+sqrt(x), with y(0)= 0
2. Find an expression for nth term of the
sequence
a) {-1, 13/24, -20/120, 27/720, ...}
b) {4/10, 12/7, 36/4, 108, ...}

1. Find the y-intercept of the curve that passes through the
point (5, 8) if,
dy/dx = 6x + 11
2. The velocity of a particle is given by the equation V = 9t^2
+ 7t where V is measured in m/min. Find the displacement of the
particle at t = 3 min if the initial displacement is 9 m.
Round your answer to the nearest whole number.

dy/dx = 2 sqrt(y/x) + y/x (x<0)
Find general solution of the given ODE

dy/dx=5y/x^3 where y(8)=e. Find the particular solution.

Find the General Solution of the Differential Equation (y' =
dy/dx) of
xy' = 6y+9x5*y2/3
I understand this is done with Bernoullis Equation but I can't seem
to algebraically understand this.

Find general solution to the equations:
1)y'=x-1-y²+xy²
2)xy²dy=(x³+y³)dx

Assume that (X, dX) and (Y, dY ) are
complete spaces, and give X × Y the metric d defined by
d((x1, y1),(x2, y2))
= dX(x1, x2) + dY
(y1, y2)
Show that (X × Y, d) is complete.

Find the general solution to the ODE y2
-10y+21=dy/dx

(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

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)

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