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Tricky. Definitely can't do it by inspection (we don't know any fuction that just differentaties to ln(x)), it's not like we've really got anything to substitute u for if we wanted to do it by substitu...

The first thing we notice is that this differential equation is seperable, meaning we can get all of our y's on the left with a dy and all of our x's on the right with a dx. Doing this by multiplying b...

1)Take the inverse sin to take x from the sin(2x):

2x=arcsin(0.5).

2)Evaluate arcsin(0.5) to get pi/6:

so 2x= pi/6

3)Dividing by 2 to simp...

When you are differentiating, use the formula:

The differential of ax^n is (n*a) x^(n-1). Or in words: 'multiply by the power, then reduce the power by 1.'

Hence for our que...

The problem with this equation lies with the denominator on the left hand side. If we recall our graph of ln(x) however, we know that ln(x) is always positive and not equal to 0. Now we can safely multipl...