How to find solutions to differential equations

And so let's see, x to the fourth divided by x, that is going to be x to the third. And so you will indeed get four x to the third is equal to four x to the third. So check, this is a solution. So is a solution. It's not necessarily the only solution, but it is a solution to that differential

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Verifying solutions to differential equations

When n = 0 the equation can be solved as a First Order Linear Differential Equation. When n = 1 the equation can be solved using Separation of Variables. For other values of n we can solve it
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Solution of First Order Linear Differential Equations

We start with differentiating in terms of the left most variable in xxyz. So here we start by taking the derivative with respect to x. First, f x = 4cos (4x+yz) Then, f xx = -16sin (4x+yz) f xxy =