Differential Equations Answers

separate the differential equation into variables

xydx + (x+1)dy=0

Solve the Non-exact Equation

v(u2+v2)du - u(u2+2v2)dv

A certain radioactive material is known to decay at a rate proportional to the amount

present. If the initially there is 50 milligrams of the material present and after two

hours it is observed that the material has lost 10% of its original mass. Find

a) An expression for the mass of the material remaining at any time t

b) The mass of the material after 4 hours

c) The time rate at which the material has decayed to one half of its initial mass

find a solution to the boundary value problem y²+4y=0 y(π/8)=0, y(π/6)=1 if the general solution to the differential equation is y(x)=c1sin2x + c2cos2x

Eliminate a and B from the equation Z=(x^2+a)(y^2+b)

ydx+2(y^4-x)dy=0

(D² +40D'² +3D' )Z=ycos x

(D^ 2 -40D' +4D'^2)Z=e^ (2x+y)

(D^ 2 -40D' +4D'^2)2=e^ (2x+y)