Differential Equations Answers

 𝑥2𝑦=1+𝑐𝑥

𝑦𝑠𝑖𝑛(𝑥) − 𝑥𝑦2 = 𝑐

Suppose it is known that the population of the community in problem 1 is 10000 after 3 years.

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 differential equation by substitution suggested by equation. Show complete solution.

du/dv =(u-v)^2 - 2(u-v) - 2

Solve the differential equation by substitution suggested by equation. Show complete solution.

(5x+3e^y)dx + 2xe^y dy =0

Solve the differential equation by substitution suggested by equation. Show complete solution.

(5x+3e^y)dx+2xe^y dy =0

Write the differential equation y'e^x + ye^2x - six = 0 in the standard form

𝑦(𝑥) = 𝑐1𝑒𝑥 + 𝑐2𝑒−𝑥 + 4𝑠𝑖𝑛(𝑥)

dy/dx + y/x =y^-2

dy/dx +xy=x sqrt y