Saturday

August 23, 2014

August 23, 2014

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

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 3:48pmI 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 3:57pmx(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

**Related Questions**

CALCULUS - Using the separation of variables technique, solve the following ...

Differential Equations - Solve the seperable differential equation for U. du/dt...

Calculus - Solve the separable differential equation: dy/dt=4y^6 and find the ...

calculus - Solve the differential equation below, given the initial condition f(...

Calculus - Solve the seperable differential equation 8yy =x. Use the following...

calculus-differential equation - Consider the differential equation: (du/dt)=-u^...

ap calculus - let y=f(x) be the particular solution for the differential ...

calculus - consider the differential equation dy/dx= (y - 1)/ x squared where x ...

ap calculus - find the particular solution y=f(x) to the differential equation ...

Calculus - 1)Find the particular solution of the differential equation xy'+3y=...