Using the formula for integration: , we get
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hi
got the problem solve the initial value problem
dy/dx=(sin(5x)+6x)/(4-cos(5x)+15x^2) when y=7 and x=0
thought i would try and use formula integration f'(x)/f(x) dx= ln(f(x))+c
i got (-1/5cos(5x)+3x^2)/(4-cos(5x)+15x^2)
= -5ln(4-cos(5x)+15x^2)
i am in real mess please help
Sorry, this is probably a silly question, but where does the 1/5 & the 5 come from (second image - 1/5 ((5 sin (5x)+6x)/(4-cos(5x)+15x^2))?
And why does (5 sin(5x)+6x) then disappear? Is something cancelling it out, or am I just not understanding the formula completely?
It's so confusing!!
Many thanks for your help,
S
You need the 1/5 because the derivative of 4-cos(5x)+15x^2 is 5sin(5x)+30x which is 5 times more than the what you are given so you multiply what you are given by 5 and multiply the whole equation by 1/5. Then using the constant multiple rule you can take the 1/5 outside when you integrate.