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Differential equations of the first and second order. Homogeneous and non-homogeneous linear differential equations

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Theoretical questions: 1. Definition of differential equations; 2. Equations with separable variables; 3. First order linear differential equation; 4. Higher order differential equations; 5. Homogeneous second-order equations; 6. Non-homogeneous second-order equations

 

Classroom assignments:

1. Solve differential equations:

1. ; 2. 3.

4. 5.

6. 7. .

8. 9.

10.

2. Find the particular solutions of differential equations:

а) ,

б) ,

2. Find the general solution of the differential equation:

1. y²-2y¢+5y=0 2. y²-y¢=0 3. y²-4y¢+3y=0
4. y²-4y¢+4y=0 5. 6.
7. 8. 9.
10. 11 12.
13. 14. 15.
16. 17. 18.

3. Find the solution of non-homogeneous second order differential equations:

1. 6. 11.
2. 7. 12.
3. 8. 13.
4. 9. 14.
5. 10.  

Homework:

Theoretical material: Numerical series. The convergence of the sum of the series.

Solve problems:

1. Solve differential equations:

1. 2.

3. 4.

5. 6.

7. 8.

2. Find the particular solutions of equations:

, .

3. Solve equations: 1. , , .

2. , , .

3. , , .

4. , , .

5. , , .

6. , , .

7. , , .

8. , , .

9. , , .


1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

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