Differential Equation Questions

Oct 2009
72
0
I'm stuck on this problem

Find the solution of the differential equation that satisfies the given initial condition. (dy)/(dx) = x/y, y(0) = -5

first i move y and x around and get y(dy)=x(dx)

then get the integral of both

y^2/2 = x^2/2 + C

multiply both sides by 2,

y^2 = x^2 + C

find C by plugging in 0 for X and -5 for Y

-5^2 = 0 + C

25 = C

I plug C into the regular equation and

then my final answer is y=sqrt( x^2 +25 )

but it is wrong. What am i doing wrong? thanks!
 
Apr 2010
384
153
Canada
I'm stuck on this problem

Find the solution of the differential equation that satisfies the given initial condition. (dy)/(dx) = x/y, y(0) = -5

first i move y and x around and get y(dy)=x(dx)

then get the integral of both

y^2/2 = x^2/2 + C

multiply both sides by 2,

y^2 = x^2 + C

find C by plugging in 0 for X and -5 for Y

-5^2 = 0 + C

25 = C

I plug C into the regular equation and

then my final answer is y=sqrt( x^2 +25 )

but it is wrong. What am i doing wrong? thanks!
Who says that's wrong? Looks A-okay to me
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
Who says that's wrong? Looks A-okay to me
If \(\displaystyle y^2 = x^2 + 25\) then surely \(\displaystyle y = \pm\sqrt{x^2 + 25}\).
 
Last edited:
Apr 2010
384
153
Canada
If \(\displaystyle y^2 = x^2 - 25\) then surely \(\displaystyle y = \pm\sqrt{x^2 - 25}\).
huh?

\(\displaystyle y^2 = x^2 + C \) with the IC \(\displaystyle y(0) = - 5 \)

\(\displaystyle 25 = C \)

\(\displaystyle y^2 = x^2 + 25 \)

\(\displaystyle y = \sqrt{ x^2 + 25} \)

?
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
huh?

\(\displaystyle y^2 = x^2 + C \) with the IC \(\displaystyle y(0) = - 5 \)

\(\displaystyle 25 = C \)

\(\displaystyle y^2 = x^2 + 25 \)

\(\displaystyle y = \sqrt{ x^2 + 25} \)

?
Sorry, I put a minus where there should have been a plus. The point is, your work was fine, you just had to make \(\displaystyle y\) the subject.
 
Oct 2009
72
0
This is one of my online homework problems, apparently y=-sqrt(x^2+25) is correct. but i still don't understand why @_@.
 

mr fantastic

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Dec 2007
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Zeitgeist
I'm stuck on this problem

Find the solution of the differential equation that satisfies the given initial condition. (dy)/(dx) = x/y, y(0) = -5

first i move y and x around and get y(dy)=x(dx)

then get the integral of both

y^2/2 = x^2/2 + C

multiply both sides by 2,

y^2 = x^2 + C

find C by plugging in 0 for X and -5 for Y

-5^2 = 0 + C

25 = C

I plug C into the regular equation and

then my final answer is y=sqrt( x^2 +25 )

but it is wrong. What am i doing wrong? thanks!
The correct answer is \(\displaystyle y = {\color{red}-} \sqrt{x^2 + 25}\), as is easily confirmed by substitution. Note that this solution satisfies y(0) = -5 ....
 
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