Wednesday
April 16, 2014

Homework Help: CALCULUS

Posted by Anonymous on Saturday, May 26, 2012 at 2:58pm.

Using separation of variables technique, solve the following differential equation with initial condition dy/dx = (yx + 5x) / (x^2 + 1) and y(3) = 5. The solution is:
a.) y^2 = ln(x^2 + 1) + 25 - ln10
b.) ln(abs(y+5)) = ln(x^2 + 1)
c.) ln(abs(y+5)) = arctan3 + ln10 - arctan3
d.) ln(abs(y+5)) = (1/2)ln(x^2 + 1) + (1/2)ln10
e.) y = ln(x^2 + 1) + 50 - ln10

Based on the initial condition y(3)=5, I know that e cannot be correct. However, I don't know where to start or how to work this out. My main problem is figuring out how to separate the variables.

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