Differential Equations : Initial-Value Problem

Please see the attached file for the fully formatted problems.

Two large containers A and B...

Two large containers A and B of the same size are filled with different fluids. The fluids in containers A and B are maintained at 0 C and 100 C, respectively. A small metal bar, whose initial temperature is 100 C, is lowered into container A. After 1 minute the temperature of the bar is 90 C. After 2 minutes the bar is removed ...continues

Find the steady state solution for ODE

Find the steady state solution for non-homogeneous ODE as found in the attached file.

First order ODE Reduced to homogeneous ODE

Given (t-3y-5) dt + (y-t+1) dy =0 introduce a change of variables to transform this ODE into a homogeneous one and solve.

Solution of the differential equation y'' + 4y = x^2 + sin x +sin 2x by method of undetermined coefficients

Solution of the differential equation y'' + 4y = x^2 + sin x +sin 2x by method of undetermined coefficients.

Solve dy/dx = -2 -y+y^2 knowing that y1= 2 is a solution.

Solve dy/dx = -2 -y+y^2 knowing that y1= 2 is a solution.

Find the interval of I (problem 39)

(See attached file for full problem description)

Verify indicated family of functions (prblm 22)

(See attached file for full problem description)

First Order IVP

First Order IVP. See attached file for full problem description.

Two problems on determination of the differential equations for water level in containers of different shapes (one cubicle and the other conical) through which water is leaking.

Water level in containers - Differential equations. See attached file for full problem description.