Differential Equations Answers

Solve the first order linear inhomogeneous differential equation using the constant variation method

(2x+1)y^,=4x+2y

Solve the first order linear inhomogeneous differential equation using the constant variation method

xy^,-2y=2x⁴

Reduce the homogeneous equation to the separated one

(x+2y)dx-xdy=0

separate the differential equation into variables

(x²-1)y^,+2xy²=0

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