Differential Equations Answers

The given differential equation (1-6y^2-3x^2y)

Solution of differential equation p^ 2 +5p+6=0 is...

a curve is such that d²y/dx²=12x-12. find the equation at point (2,9)?

(2xy-y^2+2x) dx-(2xy-x^2-2y) dy=0?

y^-2dy/dx + y^-1= 2x

(2xy-y²+2x)dx-(2xy-x²-2y)dy=0

dy/dx+ycotx=5e^cosx

A differential equation for the velocity v of a falling mass m subjected to air resistance

proportional to the square of the instantaneous velocity is:

𝑚 (𝑑𝑣/𝑑𝑡) = mg-kv²

Where k >0 is a constant of proportionality. The positive direction is downward.

(a) Solve the equation subject to the initial condition v(0)=v₀.

(b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass.

(c) If the distance s, measured from the point where the mass was released above ground, is

related to velocity v by ds/dt=v(t), find an explicit expression for s(t) if s(0)= 0.

Show that y= c₁e^x + c₂e^2x is the general solution of y’’-3y’+2y=0 on any interval, and find the particular solution for which y(0)=-1 and y’(0)=1

show that y=c1e^x+c2e^2x is the general solution of y''-3y'+2y=0 on any interval, and find the particular solution for which y(0)=-1 and y'(0)=1