Differential Equations Answers

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

1. ( y-2x)dx+xdy=0 ,y(-1)=3
2. dy=(x-4xy)dx ,y(0)= - 1/4

The integrating factor for the Bernouli differential equation 2xyy' = y^2 - 2x^3 given initial condition y(1)=2

The complementary solution for the homogeneous equation y'' + 2y' + y = 0 winll be given as