Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 6 - Differential Equations - 6.1 Exercises: 36

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