Lecture-4 - AMS 361: Applied Calculus IV (DE & BVP)...

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Outline for Lecture 4 4. Separable equations and applications The following equation is called Separable equation One can write it as So, this equation can be integrated on both sides. Although we probably most of the time to get the y=y(x) form, we can get the solution in implicit form. is the simple (but could be implicit) form of the IVP e.g. 1. Solve The solution is y(x)=7*e^(-3x^2) What if y(0) = -4? We can get the solution of y(x)=-4*e^(-3x^2). e.g. 2. Solve The solution is (y^3-5y)=4x-x^2+C It’s not possible, not practical, and not necessary to find the explicit form. If we implement IC, y(1) = 3, then we can get C=9.
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Thus, the solution becomes (y^3-5y)=4x-x^2+9. DEF: General solution : Solution with an arbitrary constant Particular solution : Solution with without the arbitrary constant Singular solution : Solution that can’t be obtained by setting the arbitrary constant. This is possible for nonlinear DE. e.g.
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Lecture-4 - AMS 361: Applied Calculus IV (DE & BVP)...

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