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Usage 1: Differential Equations - Example 2

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DCJproblemsolver.html FIRST A PRAYER: Hail Mary full of grace the Lord is with thee. Blessed are thou among women and blessed is the fruit of thy womb Jesus! Holy, Mary Mother of God pray for us sinners now and at the hour of our death! Amen! For the differential equations of the type discussed below I will also provide a link to the other problems from fields like biology and engineering where the solution methods are relavent. Hi, It's time to solve our second example problem. In it we shall verify that xsiny = cos y is a solution of (dy/dx)[xcoty + 1] = -1 As can be seen below, our solution is approached by diffentiation. The formula in question is differentiated with respect to x. Given that y is a function of x all y derivatives will have dy/dx along with them. I shall discuss the methodology line by line. The first in is the differentiation step. Notice that it is done on both sides. On the second line the result of the different...
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The Hanging Chain

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HangingChain.html Say this prayer: it helps! St. Michael the Archangel defend us in battle. Be our protection against the wickedness and snares of the Devil. May God rebuke him, we humbly pray, and do thou most Heavenly host, by the power of God cast into hell Satan and all the evil spirits who roam around the world seeking the ruin of souls. Amen. Solving the physics problem pertaining to the hanging chain. (Krantz) * .... Differential Equations for solving physics problems. * .... have method that we know to solve these equations. So, what is the classic Hanging Chain formulation. What is all that mess below? Well imagine a metallic chain hanging in the middle under the influence of gravity. In architectural terms it's a very important structure and can be mathematically described. It is in fact related to the arch, but upside down. We analyze points A (the midpoint of gravitational attraction) and B (an arbitrarily set point) on the ...
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Differential Equations: Exact Equations

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ExactEquations.html Say this prayer: it helps! St. Michael the Archangel defend us in battle. Be our protection against the wickedness and snares of the Devil. May God rebuke him, we humbly pray, and do thou most Heavenly host, by the power of God cast into hell Satan and all the evil spirits who roam around the world seeking the ruin of souls. Amen. Exact Differential Equations .... Properties: * .... know what they are right off hand. * .... have method that we know to solve these equations. First order equations can be written of the form: M(x,y)dx + N(x,y)dy = 0 (Krantz) Scientist like to find simpler ways to solve problems, and why shouldn't one method of problem solving help with another. Remember learning about circles in algebra, and that they had the form a^2 + b^2 = r^2? With r referring to radius, a family of curves (circles in this case) is designated by a specific radius. Well, it turns out that, using differential equatio...
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