Differential Equations Answers

Solve the separable differential equation for.

dy/dx= [1+x] divided by [xy^15]

Use the following initial condition: y(1)=5

y^16=?

.

Solve the separable differential equation

10x-8ysqrt(x^2 +1) * dy/dx =0

Subject to the initial condition: .y(0)=9

y=??

The differential equation

dy/dx= cos(x)(y^2 +6y+8)/(6y+16)

has an implicit general solution of the form F(x,y)=K

In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form

F(x,y)=G(x)+H(y)=K

Find such a solution and then give the related functions requested.

F(x,y)=G(x)+H(y)=

Solve the following differential equation:

(7x+8y)dx+(8x-2)dy=0

The differential equation dy/dx = 25+20x+40y+32xy

has an implicit general solution of the form F(x,y)=K

In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form of F(x,y)=G(x)+H(y)=K

Find such a solution and then give the related functions requested for

F(x,y)=G(x)+H(y)=

Find a particular solution of the differential equation: ((2y-x))/((y+2x) ) ⅆy/ⅆx=1 given that y=3 when x=2

The fourth-degree polynomial

f(x) =230x⁴ +18x³+9x² -221x-9

Has two real zeros, one in[-1,0] which is -0.0406593. Attempt to approximate this zero to within 10^-2 using the

a) secant method( using the endpoint of each Interval approximation)

b) Newton' method(use the midpoint of each Interval as the initial approximation

Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed.

Find the relative extrema using both first and second

derivative tests. f(x) = sin 2x, 0 < x < π

ydx + (1-3y)xdy = 3y²e³ydy