Solving Math Problems (Part 15)

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

Section 1.4, Problem 9

Find the general solution of the following differential equation:

Dividing by x we get:

Changing the variable using u = y/x and y' = u+ u'x, we get:

Simplifying, we get:

Integrating both sides gives:

Changing back to y gives:

Section 1.4, Problem 10

Find the general solution of the following differential equation:

xy' - y -x² tan (y/x) = 0

Dividing by x gives:

y' - (y/x) - x tan (y/x) = 0

Making a change of variable such that u = y/x and y' = u+ u'x, we get:

u + u'x - u - x tan u = 0

Simplifying and separating the variables, we have:

u' cot u = 1

Integrating we get:

ln | sin u | = x + C

Isolating the u gives:

Converting back to y we get: