DIFFERENTIAL EQUATIONS
Solutions of Systems of Linear Differential Equations
(L01.5 - 15 points) Show that the general solution of the nonhomogeneous linear system is x=(1 71}x+ []}<+[4.]e + 3' X=al_2-vzlevat +al-1 + vale-vēt + [1]{2+{2}]++ [4]
х (1 point) Find the solution to the linear system of differential equations . 3.x + 4y satisfying the initial conditions x(0) = 2 and y(0) = 1. = =c(t) = cg(t) =
4.
Solve the nonhomogeneous linear system of differential equations
2. Solve the nonhomogeneous linear system of anerential equations () u-9" (). 3. Solve the homogeneous linear system of differential equations 1 ( 2 ) uten ( 46 ) + ( ). 4. Solve the nonhomogeneous linear system of differential equations 43,742 cos(46) - 4 sin(40) (10 5 cos(40) ) +847, 7 4cos(46) + 2 sin(40) 5 sin(46) 5. Solve the initial value problem for the nonhomogeneous linear system of differential...
Solve using linear Differential
equations
1 -1 1 1. X'= 0 1 3 X 4 3 1
Find the solution to the linear system of differential equations
{?′?′==−2?+12?−?+5?{x′=−2x+12yy′=−x+5y satisfying the
initial conditions ?(0)=1x(0)=1 and ?(0)=0y(0)=0.
د (1 point) Find the solution to the linear system of differential equations { -2x + 12y -x + 5y satisfying the initial conditions x(0) = 1 y د and y(0) = 0. x(t) = yt) =
Find the general solution to the linear system of non-homogeneous differential equations x = x + x + 1 xz' = 3x1 - x2 +t
DIFFERENTIAL EQUATIONS / Linear Algebra
Only people that are proficient in DIFFERENTIAL EQUATIONS should
even attempt to solve. No beginners or amateurs allowed.
Please write clearly and legibly. No sloppy Handwriting. I must
be able to clearly and easily read your solution and answer.
Circle final answer.
9.4.12 Write the given system as a set of scalar equations. Let x' = col (x2"(t), xz '(t), xz"(t)) 1 x' = 0 1 0 0 0 1 x + -1 1 5...
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
DIFFERENTIAL EQUATIONS / Linear Algebra
Only people that are proficient in DIFFERENTIAL EQUATIONS should
even attempt to solve. No beginners or amateurs allowed.
Please write clearly and legibly. No sloppy Handwriting. I must
be able to clearly and easily read your solution and answer.
Circle final answer.
9.5.31 Solve the given initial value problem. 69 8 x'(t) = X(t), x(0) = 96 - 2 X(t) =
for
differential equations
1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...