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Determine the laplace transform for ∂u/∂t and ∂u/∂x. Hence using the laplace transform method, solve the partial differential equation ∂u/∂t=u-∂u/∂x. subject to the initial condition u(x,0)=e-7x,x>0,t>0

Apply the method of Varition of parameter

d^2y/dx^2 -4 dy/dx +3 y = 1/1+e^-x


Solve the method of undermined coefficient (D^2+8D+16)y=8e^-2x ; y(0)= 2 y'(0)= 0


what is the separable variable? dy/dx = y² sin x², y(-2) = 1/3?


2y(x^2 - y + x) dx + (x^2 - 2y) dy = 0
(D^2+2DD'+D')=e^x-y+xy

y' = csc x - y cot x


(3xy+3y-4)dx+(x+1)^2dy=0


\left(x-y\right)dx+\left(3x+y\right)dy=0


Determine the solution of the following differential equation:

xxy '= 1 + y^2


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