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 $3x^2+2y^2 =21$