Solving Math Problems (Part 5)

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

Section 1.2, Problem 15

Solve

(x ln x) y' = y

Separating the variables gives:

Integrating both sides gives:

For the right hand side, we perform a change of variable with u = ln x, du = dx / x and get:

ln | y | = ln | u | + C

Substitution ln x for u gives:

ln | y | = ln | ln | x | | + C

Taking e to the power of both sides gives:

y = C ln | x |

Section 1.2, Problem 16

Solve

Separating the variables gives

Integrating both sides gives:

Section 1.2, Problem 17

Solve

y' sin 2x = y cos 2x

Separating the variables gives:

Integrating both sides gives:

ln | y | = ln | sin 2x | + C

Taking e to the power of both sides gives

y = C sin 2x