Math Answers

The direction of a vector V(Xv,Yv,Zv) intersects a sphere on point “B”. Assuming O(0,0,0) as the centre and ‘r’ as the radius of the sphere. The mirror of the vector based on OB direction passes the point C(0,0,h). The “B” coordination, B(Xb,Yb,Zb), is required based on the above parameters.

(x+2)/3 - y+4/2 + z+1/6)= 0
(x-4/3 + y+1/4 + z--2/2) = -1
(x+1/2 + y/2 + z-1/4) = 3/4

Solve for x, y, and z.

Reduce the following PDE to a set of three ODEs by the method of separation of variables. d^2u/dr^2 +(2/r)(du/dr)+(1/r^2)(d^2u/dθ ^2) +(cot θ/r^2)(du/dθ) + (1/r^2 sin^2 θ)(d^2u/d φ^2) =0

implicit differentiation
Find dy/dx for:
a) e^cosx + e^siny = 1/4
b) e^2x+3y = x^2 -ln(xy3)

On a bike trip across the u.s Rodney notes that he covers about 190 miles every 4 days. If he continues at this rate determine about how many miles he could bike in 6 days

Solve the given differential equation by using appropriate substitution.

dy/dx = (1-x-y) / (x+y)

solve the given initial value problem. Give the largest interval I over which the solution is defined.

(1+t^2)dy/dx + x = tan^-1 t , x(0) = 4

[Hint: In your solution let u = tan^-1 t ]

Solve the given differential equation by separation of variables.

(e^x + e^-x)dy/dx=y^2

determine a region of the xy-plane for which the given DE would have a unique solution whose graph passes through a point (x0,y0) in the region

(y-x)y'=y+x

Verify that the indicated expression is an implicit solution of the given first order differential equation.Find at least one explicit solution y=Φ(x) in each case. Use a graphing utility to obtain the graph of an explicit solution.
Give an interval I of definition of each solution Φ.

2xydx+(x^2-y)dy=0 , -2x^2 y + y^2 =1