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

 № Постановка задачи 1. Постановка задачи 2. Постановка задачи 3. 0 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 1 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 2 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 3 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 4 -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 5 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 6 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 7 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 8 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 9 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 10 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 11 5x’’(t)+10x’(t)-x(t)=sin(2t2) x(0)=1, x’(0)=-1 2x’’(t)+etx(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 12 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 13 8x’’(t)-x’(t)+17x(t)=t4 x(0)=4, x’(0)=0 x’’(t)-3x’(t)+4x(t)= et, 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 14 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 15 -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 16 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 17 -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 18 14x’’(t)-10x’(t) =(2t+et)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 19 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 20 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 21 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 22 -x’’(t)+10x’(t)-x(t)=cos(2t2) x(0)=1, x’(0)=-1 2x’’(t)+etx(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 23 x’’(t)-tx’(t)+sin(t)x(t)=2t2 x(0)=-4, x’(0)=0 2x’’(t)-x’(t)= et sin(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 24 x’’(t)-8x’(t)+17x(t)=t4 x(0)=4, x’(0)=0 x’’(t)-3x’(t)+4x(t)= et, 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 25 12x’’(t)-3etx’(t)- x(t)=sin(2t4+1) x(0)=2, x’(0)=-1 3x’’(t)-x’(t)-4x(t)=2tet, 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 26 -12x’’(t)+4x’(t)-x(t)=e2t x(0)=1, x’(0)=0 -2x’’(t)+ x(t)=2 t2+e0.5t, 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 27 x’’(t)+x’(t)-2x(t)=cos(2t2)0.5 x(0)=2, x’(0)=0.1 4x’’(t)-3x’(t)+x(t) = e2t, 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 28 -9x’’(t)-x’(t)+2x(t)=sin(t2) x(0)=1, x’(0)=0 7x’’(t)-x’(t)=et 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 29 4x’’(t)-t x’(t) =(2t+et)0.3 x(0)=2, x’(0)=0 x’’(t)-13x’(t) =2 t0.5, 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 30 16x’’(t)-4x’(t)+2x(t)=t2+1 x(0)=1, x’(0)=0.3 4x’’(t)+et2x’(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