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Find the solution of the differential equation that satisfies the given initial condition.$ \frac {dy}{dx} = xe^y, y(0) = 0 $
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Calculus 2 / BC
Chapter 9
Differential Equations
Section 3
Separable Equations
Harvey Mudd College
University of Michigan - Ann Arbor
University of Nottingham
Boston College
Lectures
13:37
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.
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this question asked us to find the solution of the differential equation. Given D Y over, G axe is exceeds the why. First things first, we know we wanna put the Y stuff from often side either negative want why do y than the X stuff on the right hand side? Because now we can much more easily integrate. Integrating loft inside was simply out of negative sign. In trading the right hand side, we increase the exploited by one and then we divide by the new exponents. Now we know we're gonna be substituting an X and Y are both zero and solving for C because they've asked us that in the problem we got C is negative one. Substitute the value of C back end of negative one and simplify. We know we end up with negative. Why is natural log? We get not your logs. When you do natural of times eat, you cancel off and you simply end up with one. So that's why the E goes away is because natural times he's won. Then lastly, we want this in terms of positive. Why not negative wife? So multiply by the negative sign
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