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.

CALCULUS  Steve, Saturday, May 26, 2012 at 3:48pm
I think D is your answer, but it's a strange way to write it. It just means
y+5 = sqrt(1) * sqrt(x^2+1)
Separation of variables here is rather easy, since you have
dy/dx = x(y+5)/(x^2+1)  just divide by (y+5) and multiply by dx.
visit wolframalpha . com and type in
solve dy/dx = (yx + 5x) / (x^2 + 1), y(3)=5
it will solve the DE and if you click the Show Steps button, it will show how to separate the variables and all.

CALCULUS  Damon, Saturday, May 26, 2012 at 3:57pm
x(y+5) dx = (x^2+1) dy
x dx/(x^2+1) = dy/(y+5)
(1/2)ln(x^2+1) =
ln(y+5)+ c
if x = 3, y = 5
(1/2) ln 10 = ln 10 + c
c = (1/2) ln 10
(1/2) ln(x^2 + 1) = ln(y+5) (1/2) ln 10
(1/2) ln 10(x^2+1) = ln(y+5)
ln 10(x^2+1) = ln(y+5)^2
10(x^2+1) = (y+5)^2
Answer This Question
Related Questions
 CALCULUS  Using the separation of variables technique, solve the following ...
 Calculus  Differential Equations  Use separation of variables to find the ...
 Calculus  Differential Equations  Use separation of variables to find the ...
 PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!!  1) What are the equilibrium...
 Calculus!!  Consider the differential equation given by dy/dx = xy/2. A. Let y=...
 Differential Equations  Solve the seperable differential equation for U. du/dt...
 math  y′=(2y+x)/x, y(1)=4 1. The resulting differential equation in x and...
 Calculus  Solve the separable differential equation: dy/dt=4y^6 and find the ...
 calculus  Solve the differential equation below, given the initial condition f(...
 Math/Calculus  Solve the differential equation y'=3t^2+4. Solve the initial ...
More Related Questions