whiskybrah said:I'm completely new to differential equations. I'm just doing random problems online about them. One simple problem asks to re-arrange the following so that the x's and y's are all on one side:
\(\displaystyle x^2 + dy/dx + xy = 1\)
Can I just use algebra to do it? Like:
\(\displaystyle dy/dx = x^2/xy \)
Rearranging an equation involves isolating the variable you want to solve for on one side of the equation. This can be done by using the basic rules of algebra, such as adding, subtracting, multiplying, and dividing both sides of the equation by the same value.
Rearranging an equation allows us to solve for a specific variable or unknown value. This is particularly useful in scientific and mathematical calculations, as well as in problem-solving situations.
Yes, as long as the equation follows the rules of algebra, it can be rearranged to solve for a specific variable. However, some equations may be more complex and may require more steps to rearrange than others.
You can check your rearranged equation by substituting the values of the variables into the original equation and making sure that both sides of the equation are equal. If they are not equal, then you may have made a mistake in your rearrangement.
Some tips for rearranging equations include starting with the variable you want to solve for, being careful with negative signs, and performing the same operation on both sides of the equation to maintain balance. It is also helpful to double-check your work and simplify your final answer if possible.