Differential Equations Answers

how to solve x²y''-3xy'-2y=0

how to solve xy''+y'=0

(y/x^2)+1+1/x dy/dx=0

Solve

solve (3x^2+2xy^2)dx+(2x^2y)dy=0 where y(2)=-3

Consider ODE

(3x^2y^2+x^2)dx+(2x^3y+y^2)dy=0

Find genaral solution

(D2+3D+2)y=cos2x

The function f: R^2~{(x,y)|y=0 or y= 5x} →R

defined by

f(x,y)= x^2-3xy/(y^2+5yx)

is a homogeneous function

True or false with full explanation

Solve the following PDE using the method of separation of variables and Fourier series

u_tt = c²u_xx, 0<x<1, t<0

u(0,t) = 0, t>0

u(1,t) = 0, t>0

u(x,0) = 2x(1-x), 0<=x<=1

u_t(x,0) =0

u_tt =c²u_xx=, 0<x<1

u(0,1)=0, t >0

u(1, t)=0, t >0

u(x, 0)= 2x(1-x), (0<=x <= 1)

u_t (x, 0) =0

For high-speed motion through the air—such as the skydiver shown in the figure below, falling before the parachute is opened—air resistance is closer to a power of the instantaneous velocity v(t).

Determine a differential equation for the velocity v(t)

 of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k > 0

 for the constant of proportionality, g > 0

 for acceleration due to gravity, and v for v(t).)