Question

Which of the following is the general solution of the differential equation dy dx equals the quotient of 4 times x and y?

y2 = x2 + C

y2 = 2x2 + C

y2 = 4x2 + C

x2 − y2 = C

Answer 1

The ODE appears to be

`(\mathrm dy)/(\mathrm dx)=\frac{4x}y`

It's separable; we can write

`y\,\mathrm dy=4x\,\mathrm dx`

and integrating both sides yields

`\frac{y^2}2=2x^2+C`

`\implies y^2=4x^2+C`