Answer
The general solution satisfies the differential equation, and the particular solution is $3x^2+2y^2 =21$, at the initial condition x=1, y=3.
Work Step by Step
Start by verifying the general solution.
Take the derivative of the general solution.
$3x^2 + 2y^2 = C$
$6x+4yy' =0$
$3x +2yy' = 0$
This agrees with the differential equation.
Next plug y=3, x=1, into the general solution and solve for C
$3(1)^2 + 2(3)^2 =C$
$3+18=C$
$C=21$
Substitute C back into the general solution to find the particular solution
$3x^2+2y^2 =21$
