Differential Equations Answers

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

Solve the Bernoulli Equation "xyy'+y^2=2x"

Use appropriate substitution to reduce the following equation to a variable separable and then solve the given IVP: "dy\/dx= (3x+2y)\/(3x+2y+2), y(-1)=-1"

Show that the coefficients of the given differential equation are homogeneous and solve the given differential equation: "-ydx+(x+\u221axy)dy=0"