Differential Equations Answers

Find the general solution of the pde
(y-zx)p+(x+yz)=x^2+y^2

a substance in a chemical reaction is used up to a rate which is proportional to the amount of the substance present at any time. if 80% of the substance is used up in 4 hours, how much if the substance is left at the end of 120 minutes

Using X=x-2, Y=y+1, reduce the equation
4(x-2)^2.dy/dx=(x+y-1)^2 to the homengenous form of 1st order equation

Find the homogeneous linear differential equation with constant coefficient that has the following function as a solution x^2e^-x +4e^x

Using U= 1/2x^2 and V= 1/2y^2, solve the partial differential equation
1/x^2∂^2/∂x^2 - 1/x^3∂z/∂x= 1/y^2∂^2z/∂y^2- 1/y^3∂z/∂y

show that the Fourier series of
f(x)=e^x (-π,π)
Is
1/π sin hπ+∑_(n=1)^∞▒〖(2 sin hπ)/π(1+n^2 ) (-1)^n (cos nx-nsin nx)〗

Define the type of given partial differential equation and find the solution.
(y^2+z^2-x^2 )p+2xyq+2zx=0