Thread: Differential Equation Questions

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!

Originally Posted by break

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

Originally Posted by AllanCuz

Who says that's wrong? Looks A-okay to me

If then surely .

Originally Posted by Prove It

If then surely .

huh?

with the IC







?

Originally Posted by AllanCuz

huh?

with the IC







?

Sorry, I put a minus where there should have been a plus. The point is, your work was fine, you just had to make the subject.

This is one of my online homework problems, apparently y=-sqrt(x^2+25) is correct. but i still don't understand why @_@.

Originally Posted by break

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 , as is easily confirmed by substitution. Note that this solution satisfies y(0) = -5 ....