Solve the following first-order PDE using a change of coordinates (x, y) → (r, s): u + up 6y, u(x, 1) = 2+x,

Q: tanx V3+ts

A: According to the Leibniz rule, we have: ddx∫u(x)v(x)f(t)dt=f(v(x))·ddx[v(x)]-f(u(x))·ddx[u(x)]

Q: 3(x + 5) = 18

A:

Q: when y = In(2x – 4x). -

A:

Q: 2x + 2y = 16 4x - 2y = 8 ||

A: The objective of the question is to find the values of x and y that satisfy both equations…

Q: Evaluate for r=(3,5) , s=(-6,4) , and t=(6,-1). 2r-(s+t)=

A: Recall the following facts.

Q: Find w, where w3 = 1 + i. i? = -1.

A:

Q: 3y-6(y+z)+y

A: Distribute -6.

Q: 3y-5(3z-2y)-5z

A: This is from algebra... Expanding terms

Q: X-2y=-5, (  ,1),(3,  )

A: Given: -

Q: 3(y+7)-7y=1 y=

A: First we distribute 3.