TUGAS 12
Diffrensial Equation
Definition: The simple equation from differensial eqation is a derivative of the function of an unknown, the function itself, the variables with the name of the function is defined, and constant. If the unknown function depends on a real variable, diffrensial equation called equality differensialusual.
Diffrensial equation consists of 5 types,namely:
1. Differensial exact equation
2.Diffrensial homogeneous equation
3.Diffrensial equation that can be separated
4.Diffrensial linier equation
5.DifferensialBernoulliequation.
Diffrensial Homogeneouse Equation
Definition: Diffrenesial order equation M-1 (x, y) dx + N (x, y) = 0 dy homogeneouse said, if written in the form of derivatives (dy / dx) = f (x, y), there such a function to f ( x, y) can be expressed in the form of g (y / x).
Step-step settlement:
1. There Persamaan Diffrensial in the form of F (x, y) dx + N (x, y) dy = 0 2. Then we let y = vx 3. Persamaan form Diffrensial become dy / dx = N (x, y) / m (x, y) 4. We substitution on the value of y diffrensial with vx 5. Complete there so that only variable in the equation v diffrensial is 6. Substitution with the value v = y/x 7. So there are similarities end diffrensial results in the form of dy / dx = g (y / x) 8. To find solutions we generally diffrenetiation y = vx become so dy / dx = v + x dv / dx 9. Substitution value of dy / dx on diffrensial of dy / dx = g (y / x) with v + x dv / dx 10.Complete with integral, so generally obtained a settlement. Here I will explain about the homogeneous Persamaan Diffrensial to my friends Apriliani Erni. This activity we do on 7 January 2009. The first thing I do is first to prepare the material (material) along with sample problems and solutions. Then I tried to explain to my friends with it. I do not use the media to explain the board to my friends. My them with capital sheet of paper containing materials and sample problems, and a bolpoin. At the beginning of the explanation on the definition of a common homogeneous differensial my friend does not have difficulties, then I try to explain the steps it differensial homogeneous equality through example problems. Through examples of problems that I have given the difficulty to step-4. He felt confused why should the value of y disubstitusikan with vx. I explain why the value of y substitute vx. With the explanation that I gave my friend began to understand because this step is a requirement that equality is a form of g (y / x). I went back to continue to the next step, and my friend did not experience problems until the last step. He was so enthusiastic and the spirit of listening to the explanation I gave. After that I give to my friend's question to see if my friend already understand what I described earlier. I wait until I finished the problem and in fact he did not have difficulties during the matter. After that we return the matter Persamaan Diffrensial homogeneous together, and the end result we match together. We give each other explanations when there is a different answer.
Diffrensial Equation
Definition: The simple equation from differensial eqation is a derivative of the function of an unknown, the function itself, the variables with the name of the function is defined, and constant. If the unknown function depends on a real variable, diffrensial equation called equality differensialusual.
Diffrensial equation consists of 5 types,namely:
1. Differensial exact equation
2.Diffrensial homogeneous equation
3.Diffrensial equation that can be separated
4.Diffrensial linier equation
5.DifferensialBernoulliequation.
Diffrensial Homogeneouse Equation
Definition: Diffrenesial order equation M-1 (x, y) dx + N (x, y) = 0 dy homogeneouse said, if written in the form of derivatives (dy / dx) = f (x, y), there such a function to f ( x, y) can be expressed in the form of g (y / x).
Step-step settlement:
1. There Persamaan Diffrensial in the form of F (x, y) dx + N (x, y) dy = 0 2. Then we let y = vx 3. Persamaan form Diffrensial become dy / dx = N (x, y) / m (x, y) 4. We substitution on the value of y diffrensial with vx 5. Complete there so that only variable in the equation v diffrensial is 6. Substitution with the value v = y/x 7. So there are similarities end diffrensial results in the form of dy / dx = g (y / x) 8. To find solutions we generally diffrenetiation y = vx become so dy / dx = v + x dv / dx 9. Substitution value of dy / dx on diffrensial of dy / dx = g (y / x) with v + x dv / dx 10.Complete with integral, so generally obtained a settlement. Here I will explain about the homogeneous Persamaan Diffrensial to my friends Apriliani Erni. This activity we do on 7 January 2009. The first thing I do is first to prepare the material (material) along with sample problems and solutions. Then I tried to explain to my friends with it. I do not use the media to explain the board to my friends. My them with capital sheet of paper containing materials and sample problems, and a bolpoin. At the beginning of the explanation on the definition of a common homogeneous differensial my friend does not have difficulties, then I try to explain the steps it differensial homogeneous equality through example problems. Through examples of problems that I have given the difficulty to step-4. He felt confused why should the value of y disubstitusikan with vx. I explain why the value of y substitute vx. With the explanation that I gave my friend began to understand because this step is a requirement that equality is a form of g (y / x). I went back to continue to the next step, and my friend did not experience problems until the last step. He was so enthusiastic and the spirit of listening to the explanation I gave. After that I give to my friend's question to see if my friend already understand what I described earlier. I wait until I finished the problem and in fact he did not have difficulties during the matter. After that we return the matter Persamaan Diffrensial homogeneous together, and the end result we match together. We give each other explanations when there is a different answer.
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