contestada

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

Respuesta :

LammettHash

The ODE appears to be

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x}y[/tex]

It's separable; we can write

[tex]y\,\mathrm dy=4x\,\mathrm dx[/tex]

and integrating both sides yields

[tex]\dfrac{y^2}2=2x^2+C[/tex]

[tex]\implies y^2=4x^2+C[/tex]

Otras preguntas