# Solution of systems of differential equations

## 7.1 The solution of first-order differential equations

To find the solution of the differential equation it is necessary:

1. Specify the space variables ($SPACE$).

2. Set equation and get a solution (solveDE).

Equation with separating variables:

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Linear homogeneous equation:

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Equation in total differentials:

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## 7.2 Solution of differential equations

Procedure of solving a differential equation consists of four steps.

1. To set the ring ($SPACE$).

2. To set an equation(systLDE).

3. To set initial conditions (initCond).

4. Solving the equation(solveLDE).

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## 7.3 Solution of systems of differential equations

Procedure of solving a system of differential equations (SDE) consists of four parts.

1. To set the ring ($SPACE$).

2. To set a system of equations (systLDE).

3. To set initial conditions (initCond).

4. To get solution of SDE (solveLDE).

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In the following example, the option STEPBYSTEP = 1, gives the output of all intermediate calculations that are needed to solve this system of differential equations. Note that it does not use the command $print()$.

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Solve this system of differential equations on the accuracy e.

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The graphics solve this system of differential equations on the accuracy e.

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The graphics solve this system of differential equations.

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## 7.5 Calculation of the characteristics of dynamic objects and systems

To find the transfer function of the object, you must perform the following steps:

1. Specify the space variables ($SPACE$).

2. Ask equation input - x.

3. Ask output equation - y.

4. Obtain a solution (solveWFDS).

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To find the temporal characteristics of the object, perform the following steps:

1. Specify the space variables ($SPACE$).

2. Ask equation input - x.

3. Ask output equation - y.

4. Obtain a solution (solveTPDS).

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To find the frequency characteristics of the object, you must perform the following steps:

1. Specify the space variables ($SPACE$).

2. Ask equation input - x.

3. Ask output equation - y.

4. Obtain a solution (solveCHDS).

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