Differential Equations Answers

dx/(z^2+2y)=dy/(z^2+2x)=dz/-z

4/7x+5/14x=39

Solve the following B.V.P.

𝑢𝑡𝑡 = 𝑐 2𝑢𝑥𝑥; { 𝑢(𝑥, 0) = cos 𝑥 − 1, 𝑢𝑡 (𝑥, 0) = 0 𝑢(0,𝑡) = 0, 𝑢(2𝜋,𝑡) = 0 0 ≤ 𝑥 ≤ 2�

A string of length 10 𝑓𝑡. is raised at the middle to a distance of 1 𝑓𝑡, and then released. Describe the motion of the string assuming 𝑐 = 1𝑓𝑡. 𝑠 −1. 

The ends and sides of a thin copper bar (𝛼 2 = 1.14) of length 2 are insulated so that no heat can pass through them. Find the temperature 𝑢(𝑥,𝑡) in the bar if initially

𝑢(𝑥, 0) = { 60𝑥 0 < 𝑥 < 1 60(2 − 𝑥) 1 ≤ 𝑥 < 2 

solve the system of first-order linear differential equations

y1'=y1-y2

y'2=2y1+4y2

verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of denition of each solution. 25. x dy dx 2 3xy 5 1; y 5 e3x # x 1 e23t t d