# MIREA. Model calculations on differential equations.

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MIREA. Problem Solving Model calculations on differential equations. Option number 13.
The Moscow State Institute of Radio Engineering, Electronics and Automation
(Technical University MIREA).
Model calculations on differential equations for the students of the 2nd course. Practical problems. Part 1.
E-book (DjVu-file) contains 7 solutions of problems typical control operation (Option 13) for students MIREA. Solving problems presented in the form of a scanned handwriting collected into a single document of 13 pages, format A4. This document is stored in a format DjVu, which is open in Internet Explorer after installing utility program (plug-in). Link to download and install DjVu-plugin can be found on the company's homepage LIZARDTECH. DjVu-file containing a detailed solution of the above problems, and completely ready for viewing on your computer and print. All tasks were successfully offset MIREA teachers.
Topics solved problems.
1. Investigation of the solutions of differential equations using isoclines:
y '= cos (xy).
2. The existence and uniqueness theorem for a differential equation of the 1st order.
dx / dt = -2x (x + 1) / (t + 1).
Investigation of solutions.
3. The decision of physical problems using differential equations. (Book of problems A.F.Filippova, RHD 2000, № 91). Find time leakage of water from the cylindrical tank.
4. The solution of the linear inhomogeneous differential equation of first order (2 ways).
y '+ 2y = exp (-2x) + x exp (x)
5. The decision of the differential equation first order reduction to total differential equations. Integrating factor.
(X ^ 2-1) dx + (x ^ 2 y ^ 2 + x ^ 3 + x) dy = 0
(Book of problems A.F.Filippova, RHD 2000, № 419)
6. The solution of the nonlinear differential equation of second order. Lowering the order of the equation.
xy "- y '= x ^ 2 yy'
(Book of problems A.F.Filippova, RHD 2000, № 462)
7. The solution of the nonlinear differential equation second order of the form:
y "y + y '^ 2 - yy' = 0,5 (sinx + x).