find the general solution to the differential equation xy' + 18y = e^(x^18)
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Use the principle of superposition, and you will find that the solution for any function that is in the form [y(t) = c1e^3t + c2e^-3t is a solution for the equation. So use a function that comes back to itself after 2 derivatives, an exponential function, and with the proper exponent e^xt , the 18 will be taken care of as well! You could use e^3t, 3e^3t, or 6e^3t, and even 9e^3t. This is assuming that this function you placed is homogenous, and g(t) = 0.
i..still dont get it..
Go back to your properties of Linear Homogenous Constant-Coefficient Second Order Differential Equations. You will find out how to verify a solution or derivative, to see that they are proved to be in fact what they are, and not just something made up.