Информатика и выч. техника \ Математические модели в расчетах на ЭВМ

Решение ОДУ и краевых задач в MathCad (Практическое занятие № 2), страница 3

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Постановка задачи 1.

Постановка задачи 2.

Постановка задачи 3.

5x’’(t)+10x’(t)-x(t)=sin(2t)

x(0)=1, x’(0)=0

2x’’(t)+x(t)=sin(t),

x(0)=4, x(5)= 5

x’’ = -x’+3y

y’’ = 10x’+y-xz

z’’ = x’y-2z

x(0)=-1, y(0)=0, z(0)=1

x’(0)=1, y’(0)=0, z’(0)=0

15x’’(t)-x’(t)+x(t)=tg (2t²)

x(0)=10, x’(0)=0

x’’(t)+x’(t)+x(t)=2 t,

x(0)=4, x(4) = 3

x’ = - z +2y

y’ = 2x +y - xz

z’ = -5xy +2z - y

x(0)=1, y(0)=-2, z(0)=-1

X’’(t)-10x’(t)+x(t)=1

x(0)=1, x’(0)=2

3x’’(t)-x’(t)+x(t)= t,

x(0)=4, x(2) = 1

x’’ = -2x’- z’ +8y

y’’ = 3xy’ +2yx - z

z’’ = xy+5z-2y

x(0)=1, y(0)=-2, z(0)=-1

x’(0)=0, y’(0)=1, z’(0)=1

2x’’(t)-3x’(t)+x(t)= 2t

x(0)=2, x’(0)=1

3x’’(t)-x’(t)-x(t)=2 t,

x(0)=4, x(2) = 3

x’’ = -2x’- z’ +8yx

y’’ = 3y’ +2x - z

z’’ = 2xy+6z-2yz

x(0)=1, y(0)=-2, z(0)=1

x’(0)=0, y’(0)=-1, z’(0)=0

-x’’(t)+4x’(t)-x(t)=sin(2t)

x(0)=1, x’(0)=0

-2x’’(t)+ x(t)=2 t+1,

x(0)=4, x(2) = 2

x’’ = 4x’- 2z’ +8yz

y’’ = y’ +2yx - z

z’’ = x - z-2y’

x(0)=1, y(0)=1, z(0)=-1

x’(0)=0, y’(0)=2, z’(0)=0

x’’(t)+x’(t)-2x(t)=cos(2t)

x(0)=2, x’(0)=5

4x’’(t)-3x’(t) =2 t²,

x(0)=4, x(4) = 3

x’ = x- z +8y

y’ = 3xy +2yx - z

z’ = xy+5z-2y

x(0)=1, y(0)=2, z(0)=-1

9x’’(t)-8x’(t)-x(t)=sin(2t)

x(0)=1, x’(0)=0

7x’’(t)-3x’(t) = t²,

x(0)=4, x(4) = 3

x’’ = x’- z’ + 4y

y’’ = 3xy’ - zy - 1

z’’ = 5zx+5z - y

x(0)=1, y(0)=4, z(0)=1

x’(0)=1, y’(0)=-2, z’(0)=-1

4x’’(t)-10x’(t) =(2t)^0.5

x(0)=1, x’(0)=0

x’’(t)+3x’(t) =2 t,

x(0)=4, x(3) = 2

x’’ = 7x’ + 8z +8zy

y’’ = 6xy’ - 3yx - 5z

z’’ = 7xy + 15zy - 2y

x(0)=1, y(0)=-2, z(0)=5

x’(0)=1, y’(0)=-2, z’(0)=0

x’’(t)-4x’(t)+2x(t)=t²+1

x(0)=1, x’(0)=4

4x’’(t)+2x’(t)-x(t) = t²,

x(0)=4, x(4) = 3

x’’ = -2x’- z +8y

y’’ = 3xy’ +2yx - z

z’’ = xy+5z’-2y

x(0)=1, y(0)=-2, z(0)=-1

x’(0)=1, y’(0)=-2, z’(0)=-1

x’’(t)-18x’(t)+6x(t)= 2t+10

x(10)=1, x’(10)=5

x’’(t)- x (t) =2 t²,

x(0)=1, x(1) = 0

x’’ = -2x’- z +8y

y’’ = 3xy’ +2yx - z

z’’ = xy-4z’

x(0)=1, y(0)=-2, z(0)=4

x’(0)=1, y’(0)=2, z’(0)=0

3x’’(t)-x’(t)+3x(t)= 2t+sin(t)

x(2)=1, x’(2)=0

10x’’(t)-3x’(t) =5-2 t²,

x(0)=4, x(3) = 2

x’’ = 9x’- 8z +4y

y’’ = 3y’ +2yx – z’

z’’ = x’y + 5z - 4z’

x(0)=1, y(0)=4, z(0)=4

x’(0)=1, y’(0)=1, z’(0)=1

5x’’(t)+10x’(t)-x(t)=sin(2t²)

x(0)=1, x’(0)=-1

2x’’(t)+e^tx(t)=cos(t),

x(0)=4, x(5)= -2

x’’ = -x’+3y+xyz

y’’ = 10x’+y-xz

z’’ = x’y-2z-xy’

x(0)=-1, y(0)=0, z(0)=-1

x’(0)=1, y’(0)=0, z’(0)=1

5x’’(t)-x’(t)+sin(t)x(t)=2t²

x(0)=4, x’(0)=0

-2x’’(t)+x’(t)= sin(2t³),

x(0)=-2, x(4) = 3

x’ = -z+ z’ +2y

y’ = 5x +7y - 5x’z’

z’ = -3xy +2z - y

x(0)=1, y(0)=-3, z(0)=-1

8x’’(t)-x’(t)+17x(t)=t⁴

x(0)=4, x’(0)=0

x’’(t)-3x’(t)+4x(t)= e^t,

x(0)=4, x(2) = 1

x’’ = -x’- z’ + x’y’z +8y

y’’ = 13xy’ +2y’x - z

z’’ = xy+5z’-12y

x(0)=1, y(0)=-2, z(0)=-1

x’(0)=0, y’(0)=2, z’(0)=1

12x’’(t)-3x’(t)- x(t)=2t⁴+1

x(0)=2, x’(0)=-1

3x’’(t)-x’(t)-4x(t)=2t,

x(0)=4, x(2) = 1

x’’ = x’- 4z’ +7y’x’

y’’ = 13y’ -2x + z’

z’’ = 2xy+6z-2yz

x(0)=1, y(0)=-2, z(0)=1

x’(0)=0, y’(0)=1, z’(0)=0

-3x’’(t)+4x’(t)-x(t)=sin(2t)

x(0)=1, x’(0)=0

-2x’’(t)+ x(t)=2 t+1,

x(0)=4, x(2) = 2

x’’ = 4x’- 2z’ +8yz

y’’ = y’ +2yx - z

z’’ = x - z-2y’

x(0)=1, y(0)=1, z(0)=-1

x’(0)=0, y’(0)=2, z’(0)=0

x’’(t)+x’(t)-2x(t)=cos(2t) t²

x(0)=2, x’(0)=5

4x’’(t)-3x’(t)+x(t) = t²,

x(0)=4, x(4) = 0

x’ = 2x- yz +8y’

y’ = 6xy +2yx - z

z’ = 7xy+15xyz’-2y

x(0)=1, y(0)=2, z(0)=-1

-9x’’(t)-x’(t)+2x(t)=sin(t²)

x(0)=1, x’(0)=0

7x’’(t)-13x’(t) = t²,

x(0)=4, x(4) = 5

x’’ = x’- z’ + 4y

y’’ = 3xy’ - zy - 1

z’’ = 5zx+5z - y

x(0)=1, y(0)=4, z(0)=1

x’(0)=1, y’(0)=-2, z’(0)=1

14x’’(t)-10x’(t) =(2t+e^t)^0.5

x(0)=2, x’(0)=0

x’’(t)-3x’(t) =2 t⁵,

x(0)=4, x(3) = 2

x’’ = -7x’ + z +8z’y

y’’ = x’y’ - 3yx - 5z’

z’’ = xy + 15z’y’ - 2y

x(0)=1, y(0)=-2, z(0)=3

x’(0)=1, y’(0)=-2, z’(0)=0

6x’’(t)-4x’(t)+2x(t)=t²+1

x(0)=1, x’(0)=3

4x’’(t)+2x’(t)-x(t) = t²,

x(0)=4, x(3) = 2

x’’ = -2x’- y’z’ +8y

y’’ = 3xy’ +2yx - z

z’’ = xy+5z’-2xyz’

x(0)=1, y(0)=-2, z(0)=-1

x’(0)=1, y’(0)=2, z’(0)=-1

x’’(t)-8x’(t)+6x(t)= (2t+10)^0.5

x(10)=1, x’(10)=5

x’’(t)- 5x (t) =4 t⁴,

x(0)=1, x(1) = -1

x’’ = -2x’- xy’z +8yz’

y’’ = 3xy’ +2yx - z

z’’ = xy-4yz’

x(0)=1, y(0)=-2, z(0)=-4

x’(0)=1, y’(0)=2, z’(0)=0

3x’’(t)-x’(t)-7x(t)= (2t+sin(t))^0.5

x(2)=1, x’(2)=-5

10x’’(t)-3x’(t) =5-2 t²,

x(0)=-4, x(3) = 2

x’’ = 9x’y- 8z’ +4x’y’

y’’ = 3y’ +2yx – z’

z’’ = x’y + 5z – 4xyz’

x(0)=1, y(0)=3, z(0)=4

x’(0)=1, y’(0)=1, z’(0)=1

-x’’(t)+10x’(t)-x(t)=cos(2t²)

x(0)=1, x’(0)=-1

2x’’(t)+e^tx(t)=½COS(t)½,

x(0)=4, x(5)= -2

x’’ = -7x’+13y+xy’z’

y’’ = 10x’+y-xz

z’’ = x’y-2z-x’y’

x(0)=-1, y(0)=3, z(0)=-1

x’(0)=1, y’(0)=2, z’(0)=1

x’’(t)-tx’(t)+sin(t)x(t)=2t²

x(0)=-4, x’(0)=0

2x’’(t)-x’(t)= e^tsin(2t³),

x(0)=4, x(4) = 3

x’ = -xy’z+ z’ +2y

y’ = 5x +7yz’ - 5x’z’

z’ = -3xy +2z - y

x(0)=1, y(0)=3, z(0)=-1

x’’(t)-8x’(t)+17x(t)=t⁴

x(0)=4, x’(0)=0

x’’(t)-3x’(t)+4x(t)= e^t,

x(0)=4, x(2) = 1

x’’ = -x’- z’ + x’y’z +8y

y’’ = 13xy’ +2y’x - z

z’’ = xy+5z’-12y

x(0)=1, y(0)=-2, z(0)=-1

x’(0)=0, y’(0)=2, z’(0)=1

12x’’(t)-3e^tx’(t)- x(t)=sin(2t⁴+1)

x(0)=2, x’(0)=-1

3x’’(t)-x’(t)-4x(t)=2te^t,

x(0)=4, x(2) = -1

x’’ = x’- 4z’ +17x’yz

y’’ = 13y’ -2x + z’

z’’ = 2xy+6z-2yz

x(0)=1, y(0)=-2, z(0)=-1

x’(0)=0, y’(0)=1, z’(0)=0

-12x’’(t)+4x’(t)-x(t)=e^2t

x(0)=1, x’(0)=0

-2x’’(t)+ x(t)=2 t²+e^0.5t,

x(0)=4, x(2) = 2

x’’ = 4x’- 2z’ +8yz

y’’ = y’ +2yx - z

z’’ = 7x -8z-2y’z’

x(0)=1, y(0)=1, z(0)=-1

x’(0)=0, y’(0)=2, z’(0)=2

x’’(t)+x’(t)-2x(t)=cos(2t²)^0.5

x(0)=2, x’(0)=0.1

4x’’(t)-3x’(t)+x(t) = e^2t,

x(0)=4, x(4) = 0

x’ = 2x- x’yz +8y’z’

y’ = 6xy +2yx - z

z’ = 7xy+5xyz’-2y

x(0)=1, y(0)=2, z(0)=-1

-9x’’(t)-x’(t)+2x(t)=sin(t²)

x(0)=1, x’(0)=0

7x’’(t)-x’(t)=e^t sin(t²),

x(0)=-0.4, x(4) = 0.5

x’’ = x’- z’ + 4y

y’’ = -3xy’ – z’y - 1

z’’ = 5zx+5yz’ - y

x(0)=1, y(0)=4, z(0)=1

x’(0)=1, y’(0)=1, z’(0)=1

4x’’(t)-t x’(t) =(2t+e^t)^0.3

x(0)=2, x’(0)=0

x’’(t)-13x’(t) =2 t^0.5,

x(0)=4, x(3) = 2

x’’ = -7x’ + z +8z’y

y’’ = x’y’ - 3yx - 5z’

z’’ = 6xy + 15z’y’ – 2z

x(0)=1, y(0)=-2, z(0)=3

x’(0)=1, y’(0)=-2, z’(0)=0

16x’’(t)-4x’(t)+2x(t)=t²+1

x(0)=1, x’(0)=0.3

4x’’(t)+e^t2x’(t) = t²,

x(0)=4, x(3) = 0

x’’ = -2x’- y’z’ +8y

y’’ = 3xy’ +2yx - z

z’’ = xy+5z’-2xyz’

x(0)=1, y(0)=-2, z(0)=-2

x’(0)=1, y’(0)=2, z’(0)=-1

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