Go ahead and do so now by switching to Mathematica, typing it outĪnd hitting. (Note the double equals sign, which is used since we're entering an equation Information " DSolve, x]" (among other things.)Īrmed with all of the above information we should feel comfortableīy entering the following command: DSolve^2 Cos y', y,x] It's been a while now since we asked for the syntax of the DSolveĬommand, so I'll just remind you. The sine function takes the form Sin, and theĬosine function takes the form Cos, where you fill in the dots a+b=5 wouldĮquals sign is used when forming equations, including differential Logical operator comparing both sides of the equality to decide on whether Used in the session, the current value of w at that Immediately moved into v, but instead a "pointer" to The next time u is used in the session, 7 is used in its Want to move a value into a variable so that the variable has that value We usually don't bother to distinguish between when writing them on paper: Mathematica has three different versions of the equals sign that We're about to feed this equation into Mathematica's DSolveĬommand, but first a few notes and reminders of what we learned in the introductory labs: To achieve the change we divide the originalĪnd replace the ( dy/dx) by the notation y′ Must be put in derivative form, whereas in the original differential equation We're here to learn about Mathematica's differentialīefore we can use the DSolve command the differential equation Root of both sides, and then the arcsine,) but that's not our main concern Made explicit with a little work, (multiply both sides by 3, take the cube Notice that we have supplied the C ourselves. Anyway, looking over your results, and setting both sides equal to oneĪnother, you should realize that the (implicit) solution to the original It is worth noting here that Mathematica's integration of the right-hand side of the differential equation takes on a far different form from the result you would most likely get if you were to evaluate the integral by hand, (most likely by using substitution.) This kind of behavior is quite typical of most computer algebra systems, and can be fairly frustrating at times. Mathematica leaves off the constants of integration, so we must supply Mini-session you just had should have looked something like this: Did you get that right hand side figured out? The Mathematica
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