Linear equation Definition and 131 Threads

Homework Statement Solve the following differential equations. 3xy'+y=12 Homework Equations I believe this is a linear equation problem. So I believed to have solved it, however I am not sure if I have done so correctly. The Attempt at a Solution

can this equation y, = ycot(x) + sin(x) be reduced to a homogenous linear format? If yes, how? I tried the usual y=xv and the x=X+h, y=Y+k but doesn't seem to be working. Any ideas? Thanks just realized its in the form of dx/dy+Px=Q so I solved it by multiplying on B.S. by e∫Pdx and the...

Homework Statement solve 4y''-4y'+y=16et/2 Homework Equations v1= -∫ y2g/w v2= ∫ y1g/w The Attempt at a Solution http://imgur.com/gxXlfdH the correct answer is 2t^2 e^(t/2) instead of what i have though, i am not sure what i am doing wrong?

Fint the exact solution of the system dy/dt = -15y-25z dz/dt=-47y-85z with inital condition y(0)=2, z(0)=5 either by writing the equation in matrix form as dx/dt =AX where x=(y z) and diagonalising the matrix A, or otherwise. Using fortran programming with second order adam bashforth...

3x + 4y + 2y = 1 The solutions for x, y, and z is { ( (1/3-4l-2m) | 3l | 2m ) }, where y = l and z = m. I've tried this method, presupposing y = l and m = z, then it came to I. l = (1 - 3x -2m) / 4 II. m = (1 - 3x -4l) / 2 If I try to put in either (I) or (II) to x, it would come...

Find the gernal solution of cosx\frac{dy}{dx}+(sinx)y=1 So \frac{dy}{dx}+\frac{sinx}{cosx}y=\frac{1}{cosx} \frac{dy}{dx}+tan(x)y=csc(x) therefore P(x)=tan(x) Let \mu (x) = e^{\int P(x) dx}=e^{\int tan(x) dx} =\frac{1}{cosx} multiply both sides of the equation by integrating factor...

Homework Statement Solve x,y and z from \frac{y+z}{a}= \frac{x+z}{b}=\frac{x+y}{c} = xyz wit a,b,c not equal to zero. Homework Equations The Attempt at a Solution I have no idea how to start. I've tried several things but it seems like I'm missing something. I did find the trivial solution...

1. The problem estatement, all variables and given/known data Find the Linear equation of a plane passing through the origin and points (6,2,2) and (5,-1,1) Homework Equations Linear equation of a plane takes the form ax+by+cz+d = 0 The Attempt at a Solution So I believe I can...

Hello! The following system of linear equations has been expressed in term of column vector in the following. . How can I express the system of linear equations in term of row vector? In addition, What is the field of scalars? I would request to explain it. Thanks in advance.

write a linear equation in 3 variables that is satisfied by all 3 of the given ordered triples $(1,1,1), (0,2,0), (1,0,0)$ the examples in book are all on the $ax+by+cz=d$ equation but with just ordered triples there is no $d$ or can it be found from them... otherwise I would solve this by...

hey good people, I'm having a problem with how to solve a problem I'm having. first of all, I am working on an isometric game, and align my tile's are layed out like so: so, here's the problem: the numbers are arranged in how the tile's are layed out in memory, however, i want to be...

15+1/2=0.60(20x)

My questions concerns the information in the document. I highlighted the portion that is confusing me and a sample problem at the bottom. Question: Look at the equation 2.2.4 in the document. When I set the function u equal to zero the equation becomes 0 = 0 + 0 + f(x,t) or f(x,t) = 0. Now...

Homework Statement Alright... 3x - 6y = 0, Graph the linear equation, finding it's intercepts. Homework Equations I've tried solving it by putting 0 in for x / y, and I've also tried putting -2 in for x / y, so that y = 2 when I move it over, and the system for my college...

Homework Statement Solve: dP/dt + 2tP = P + 4t - 2 The Attempt at a Solution I've done a couple of these but I'm not sure how to start with this one... First I have to put it in standard form right? dP/dt + P(2t - 1) = 4t - 2 Then obtain the integrating factor by...

Homework Statement The age of a mother is twice the sum of ages of her 2 sons. 5 years later the mother will be 20 years older than the sum of ages of her sons. What age is the mother today? Homework Equations The Attempt at a Solution M - mother ; S1 = son1 ; S2 = son2. S = S1...

Homework Statement Show that if the linear equations x1 + kx2 = c and x1 + lx2 = d have the same solution set, then the equations are identical ( k = l, c = d) The Attempt at a Solution since the two equations have the same solution set, they are equal for every value of c and d so x1 +...

Is it? Personally, I think it is since the max power on any unknown is 1, no trig function, no product of unknowns etc. Also could the above mentioned linear equation form a linear system ? I don't think so (cause we always need at least two separate linear equations to form a linear system) but...

Hello guys, i hv doubt in this question: "1-Mark the point Q, such that the line through P (1, -2) and Q is perpendicular to the x-axis (the horizontal axis) so that the point Q to point P is equidistant from the axis x. Find the equation of the line."If the line be perpendicular of the X...

Good Day, I need some help with the following problem. I do not know how to generate a linear equation connecting y and x from the expression below as the 4 seems to complicate things \(3^y = 4(3^{x-2}) - 1\) Could some one please care to give me some advice? Thanks in advance.

Homework Statement Consider the following linear system of equations: x1+2x3-5x4 = 0 x1 + 4x2 +4x3 – 5x4 = 10 x1 + 2x2 + 3x3 – 5x4 = 5 4x1 + 2x2 + 9x3 – 20x4 = 5 b) Solve the equation system with the Gaussian method. c) The solution set describes a plane. Specify it in the parameter...

I took a picture of a simple problem from my Diff Eq book. It is split up into two pictures for better resolution. In summary, ty'+2y=4t^2 (1) Has the solutions, y=t^2+C/t^2 (2) So, equation (1) has infinite solutions of the form of (2). But imposing the initial...

Hello, I want to maximize a linear equation: 4*a + 8*b + 7*c + 5*d + 9*e with the following constraints: 0<=(4*a + 8*b + 7*c + 5*d + 9*e)<=1 0<=a<=100; 0<=b<=100; 0<=c<=100; 0<=d<=100; 0<=e<=100 Can I solve this problem using linear programming? Is there are any other method to do it...

Homework Statement Suppose v is a vector satisfying: \alpha v + ( a \times v ) = b For \alpha a scalar and a, b fixed vectors. Use dot and cross product operations to solve the above for v. Homework Equations The unique solutions should be: v=\frac{\alpha^{2}b- \alpha (b \times a) + (b...

Homework Statement Find the function satisfying the differential equation: dy/dx - 3y = 6e^(5x) with y(0) = -6 Homework Equations I believe this is Linear, so it is dy/dx + P(x)y = f(x) The Attempt at a Solution I chose -3y to be P and used it to obtain integrating factor e^(-3x). I...

Homework Statement Ok, so I have an unknown exponential function: y1 = f1(t) By measuring the values of t and yi, a linear connection is generated between Yi (=log (yi)) and t: Yi = Ait + Bi. A1 = -2.12 B1 = 1.96 Problem 1: Describe f1 in the following matter: y1 = f1(t) = Ceλt...

I am currently trying to solve for the metric function for a black hole in adS space with quasi-topological gravity. The details aren't too important, but the point is that I have to solve for a cubic at one point, and choose the correct solution, which is the one that reduces to a linear...

Homework Statement The question is asking whether or not the given equations are linear. I am unsure whether this equation (below) is linear or not? x1 + 5x2 - sqrt(2x3) = 1 The Attempt at a Solution My initial answer is that it is not due to the fact that a linear equation does...

Let a be a fixed nonzero vector in R^n a. Show that the set S of all vectors x such at ax=0 is a subspace of R^n. b. show that if k is a nonzero real number, then the set A of all vectors x such that ax=k is an affine subspace of R^n, but not a linear subspace.how do i even show this.. I am so...

show that S and T have the same span in R^3 by showing that the vectors in S are in the span of T and vise versa. S= {(1,0,0), (0,1,0)} T= {(1,2,0), (2,1,0)}im a little confused on how to start off on this problem.. help?!

Please anyone can help me for finding solution of linear equation by using mathematica, for example take us equations as, 9x+10y+7z+18 w=8 3x-3y-8z+88 w=0 12x+9y-17z-14w=2 x+y-2z+w=0 Infect I have to use this thing in my code which will be good by using this thing,,, Any...

Hi, I have a differential equation that I just can't seem to solve. Now here's the deal: I'm sure there are advanced methods that would easily solve this equation, but the equation is in the chapter on First-Oder Linear Equations, so it shouldn't be anything fancy. There's even a hint: it...

Hi, How can I solve the equation below for M. G*inv(A+G'*inv(M)*G)*G'+F+M=0 G' is the transpose of G and inv(.) is the inverse of a matrix. Thanks

Hello Everyone, I was wondering if there is a statistical method to compare two linear equations. I have one "nominal" equation y1=a1*x+b1 and one equation found using linear regression on a data set, y2=a2*x+b2. I know I can just "look" and compare the slope and intercept values but it...

Homework Statement Find the general solution of the differential equation: y'' + 4y' + 13y' = 169x + 81e^{e-2x} EDIT: Can't get latex to work.. so : http://mathbin.net/60293 The Attempt at a Solution 13Ax + 4A + 13B + 9Ce^{-2x} = 169x+81e^{-2x} http://mathbin.net/60294 Now i have no clue...

1) Let A be an n x n matrix. Prove that if Ax= 0 for all n x 1matrices, then A=O. Can you show me the steps of solving this problem? Please!

So i have (r^4)-16 = 0 r^4 = 16 r = 2 So i only have one root As the general solution i have y = C(sub1) * (e^(2x)) + C(sub2) * (e^(2x)) Is this correct? If not please lead me in the right direction

Homework Statement Determine an equation of a line through -3,5 and 1, -3 so... What i got is y - 5 = -2(x-(-3) ) So that turns into y - 5 = -2x + 3 correct? now i am suppose to simplify, and the answer is y = -2x -1 how did they get y = -2x -1 from y - 5...

Homework Statement Question: For a certain commodity the supply equation is given by: S = 2p + 5 At a price of $1, there is a demand for 19 units of the commodity. If the demand equation is linear and the market price is $3, find the demand equation ? Homework Equations...

**Quick: Just a SIMPLE question on Linear equation. Homework Statement Ok, 5x + 2(30) = y turns into: 5/3x + 20 = y (that is 5 over 3 x) Now it says something I don't understand. "We now have two equations: y = 5/3x + 20 and y = x + 30 (How did it get y = x + 30?)...

Homework Statement Find value L and X. 0.182(L2+X2)=1602 0.182[(555.56+L)2+X2]=2402

How do I show the difference of two solutions of an inhomogenous linear equation Lu=g with the same g is a solution of the homogenous equation Lu=0. Your help is much appreciated. thanks a lot.

Hey all. Looking at "Pattern Recognition and Machine Learning" (Bishop, 2006) p28-31, the author appears to be using what would ordinarily be a delimiter for a conditional probability inside a linear function. See the first variable in normpdf as below. This is in the context of defining a...

For the system of linear algebraic equations: x − y = 1 2x + 3y = 7 a) find solution by the Cramer’s rule; b) find solution by the method of Gaussian elimination; c) write the first iteration of the Jacobi method with the initial guess x^0=y^0=1. I understand Cramer's Rule, and I think...

1) Is there any way to find integer solutions for a linear equation ax+by=c, with a,b,c known and without having an another equation to substitute in the above one. ex : 3x+y=394; Is there any worst case for c being very large. 2)Is there any easy and fastest way to get...

Homework Statement if a+11b is completely divisible by 13 and a+13b is completely divisible by 11 then find the the smallest possible value of a+b. a and b are positive integers. the answer is 28 Homework Equations a+11b= 13x a+13b= 11y The Attempt at a Solution i have equated...

Homework Statement P = -50Qd + 80 P = 2Qs + 10 P = Price Qd = Quantity demanded Qs = Quantity supplied Find the equilibrium Price and Quantity. Homework Equations Qd = Qs (equilibrium) The Attempt at a Solution Qd = Qs Q Since they both equal to P -50Q + 80 = 2Q + 10...

My problem is not knowing the effects of modulus in parts of an equation ( in this case linear ) on the parts of the graph. An elaboration will be like y = |bx| + c , what's the effect on the graph compared to y = bx + c and likewise : y = bx + |c| and y = bx + c or even y = b|x| + c compared to...

Homework Statement I have a matrix [11x10] which I want to solve (Ax=b). Matlab comes with an answer, but I would like to know if there is a possibility to give boundary conditions to this problem. like x_i can't be greater than 300 or something. is it possible to restrict the outcome?2. The...

Is there anyway I can convert the attached equation into a linear relationship so that 'a' is the gradient of the straight line. 't' and 'h' are both variables. It doesn't matter exactly what the x and y values are. I just need 'a' to be the gradient of the straight line. I tried lots of...