Here is a two-step process that works every time:
1). From a book, a teacher, or a knowledgeable acquaintance, learn the permissible operations.
2). Apply the operations according to the rules you have learned.
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Some differential equations can become a simple algebra problem. Take the Laplace transforms, then just rearrange to isolate the transformed function, then look up the reverse transform to find the solution.
That completely depends on exactly what operation you have in mind. You can "do" several different types of operations to an equation, such as solve it, differentiate it, rearrange it, factor it, or apply the same arithmetic procedure to both sides of it. But you can't "do" the equation.
You need to make the terms on each side as much alike as possible in the two equations for easy thought process. For example, Let us look at the following two equations. a * b = c * d --- (1) x * d = k * a --- (2) Rearrange (2) so that 'd' is on the right side of the equation and 'a' on the left. a * k = x * d --- (3) Divide (1) by (3): b / k = c / x --- (4) I have eliminated two variables from (1) and (2) to form equation (4). ===========================
Rearrange the second equation to read 2x - y = -3Add the two equations: 3x = 6:Divide by 3: x = 2 so y = 7
Equivalent equations are equations that have the same solution set.