But this simple equation can easily be solved, as it is a separable equation. Dividing both sides of it by and integrating we get: Integrating by substitution the integral on the left hand side is simply. Thus pulling over the natural logarithm to the right, we have: This is very important and is called the 'integrating factor'. So our original ODE can be rewritten as But now the whole point of introducing was we were trying to turn the left hand side of this ODE into for easily integrating it, which is exactly what we have done. Thus So we may integrate both sides and then solve for y to get Below we provide another derivation of this formula. Step-by-Step Solution [ edit] Example 1: P and Q are Constant [ edit] Let's say we have the equation where n and m are constants. Solve this for y. Step 1: Find the integrating factor,, with P(x) = m and the integration of a constant being yielding is collapsing into C. Letting C=1, we get e mx. Step 2: Multiply through by the integrating factor just found.
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*You will get your 1st month of Bartleby for FREE when you bundle with these textbooks where solutions are available ($9. 99 if sold separately. ) After your trial, your monthly subscription will automatically continue at $9. 99 each month. You can cancel at any time. Publisher Info Publisher: Cengage Learning Published: 2016 Summary Author bio Table of contents Digital rights Suitable Devices - Hardware known to be compatible with this book. Note: Reader software still needs to be installed.
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