Help with simple differential equations y dy= x dx.?
I am told to find a solution of the differential equations y dy= x dx. What I did is integrate left and right hand side respectively end up with y^2=x^2+2c when its all cleaned up. The solution book says I should get is x^2y^2=C and I can see how I can get y^2x^2=C but not x^2y^2=C like book has.

answers:
Jeffrey K say: Your answer is correct and so is the book. Multiply your equation by 1. Since c is an arbitrary constant, you can let C = c and you match the book.

alex say: integrate both side
y² = x² + C
or
y² + C= x²

Φ² = Φ+1 say: y²  x² = C₀
(y²  x²) = C₀
y² + x² = C₁
x²  y² = C₁

Mike G say: It just means that the Cs will have opposite signs.

Como say: :
Integrate
y²/2 = x²/2 + C
y² = x² + 2C
y² = x² + K
y = [ x² + K ] ^(1/2)

Captain Matticus, LandPiratesInc say: They're essentially the same, because you don't have a specific value for C
1) y^2 = x^2 + C
2) y^2  x^2 = C
3) x^2  y^2 = C
The C in 2 is not the same as the C in 3. Your math is good, if that's any comfort.

King Leo say: .
it’s just algebra somehow
y dy = x dx
y dy  x dx = 0
∫ y dy  ∫ x dx = ∫ 0
½y²  ½x² = c
y²  x² = 2c
y²  x² = C
—————
y dy = x dx
0 = x dx  y dy
∫ 0 = ∫ x dx  ∫ y dy
c = ½x²  ½y²
2c = x²  y²
C = x²  y²
x²  y² = C
—————
