Differential Equations Answers

Find the constants C0, C1, and x1 so that the quadrature formulae z0^1 f(x) dx = C0 f(0) + C1 f(x1),

Has the highest possible degree of precision

form a partial differential equation for (x− a)² + (y−b)² + z² = 1

(x− a)² + (y−b)² + z² = 1

Solve the differential equation 

dy/dx=x/16y

.

a) Find the implicit solution

b) Find the equation of the solution through the point (x,y)=(4,1) Your equation must describe a single curve of y=f(x) with the domain of f as large as possible. 

c) Find the equation of the solution through the point (x,y)=(0,−2) Your answer should be of the form y=f(x)

Find the equation of the solution to dy/dx = x^(5) * y through the point (x;y)=(1;2)

Find a solution to dy/dx=xy+9x+4y+36

If necessary, use K to denote an arbitrary constant.

Find u from the differential equation and initial condition.

du/dt= e^(1.5t-1.3u), u=0 1.3

Find u=?

Find a function y of x such that

9yy'=x and y(9)=10

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=??