Solving Math Problems (Part 9)

More problems from Advanced Engineering Mathematics, 6th Edition by Kreyszig.

Section 1.2, Problem 27

Solve the initial value problem:

L(dI/dt) + RI = 0 with I(0) = I₀

This is a problem out of electric circuit analysis.  We separate the variables to get:

Integrating both sides gives:

ln | I | = (R / L) t + C

Raising e to the power of both sides gives:

Solving for the given initial condition, we find the C = I₀ and the solution is:

Section 1.2, Problem 28

Solve the initial value problem:

v(dv/dx) = g = const with v(x₀) = v₀

We can proceed directly to integrating both sides:

∫ v dv = ∫ g dx

½v² = x g + C

Using the given initial condition, we solve for C to find C = ½(v₀² - 2 x₀ g) and the solution is: