Question

Find the general solution of the differential equation dy/dx = xeˣ² - ln(y²)).

a) y = eˣ² + C
b) y = sqrt(eˣ² + C)
c) y = +/- eˣ²
d) y = +/- sqrt(eˣ² + C)

Answer 1

To find the general solution of the given differential equation, separate the variables and integrate. The correct answer is d) y = +/- sqrt(e^(x^2) + C).

Step-by-step explanation:

To find the general solution of the given differential equation, dy/dx = xe^(x^2) - ln(y^2), we need to separate the variables and integrate.

If we rewrite the equation as:

2ln(y)dy = xe^(x^2)dx

Then integrating both sides:

∫2ln(y)dy = ∫xe^(x^2)dx

We can solve these integrals and find the general solution for y.

The correct answer is d) y = +/- sqrt(e^(x^2) + C).