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SOLVE PARTIAL DIFFERENTIAL EQUATION- xP+yQ=3Z

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Posted on Jan 02, 2017

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SOURCE: 2x -y +z -w =

You have to put the equations into matrix form first. To do this, each variable has one column in the first matrix and you fill in the co-efficients for the variables. The second matrix has one column and contains all the numbers.

{ 2 -1 1 -1} = Matrix A
{ 1 3 -2 0}
{ 3 -2 0 4}
{-1 -3 -3 -1}

{-1} = Matrix B
{-5}
{ 1}
{-6}

{x=-2} = A*(B^-1)
{y=-.2}
{z=3}
{w=1/6}

I used excel for all my calculation and a helpful tutorial can be found here. I hope this helps and have a nice day!

Posted on May 05, 2011

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Examples of homogeneous differential equation


Hi janeth sabay,

 

Have a good day!!

 

Here is your needed example for Homogenous differential equation:

 

The equation 49e8abf8a1c5be91fadbf33a5405bdc3.gif is said to be homogeneous if P and Q are homogeneous functions of x and y of the same degree.

cc966bdc4bb845d781e46c1ccf986b02.gif(1)

We can test to see whether this first order equation is homogeneous by substituting 21fe29cd49ecbd3abe2ae6373e89eab6.gif . If the result is in the form f(v)i.e. all the x's are canceled then the test is satisfied and the equation is Homogeneous.

Example 1:19c981882c1f9b05fadf586b56a931bc.gif(2)

d8be3b3ee65102c9f51076f6fbf371a4.gif(3)

There are no terms in x on the right hand side and the equation is Homogereous.Example 2:72f80f87eb510a9e0fd81c423b3faa55.gif(4)

b8821dedcc10e7738d072f6f0e2b7585.gif(5)

So the original equation is not homogeneous.Methods Of Solution.

A solution can be found by putting y = vx on both sides of the equation:-

Example 3:

fa23f299c6866eb1139d14429d91ce12.gif(6)

Putting y - vx

Since y is a function of x so is v

d362aad60b6e62347861fab3ab05ab83.gif(7)

e347d11784544bf8765eda8bd3aa2157.gif(8)

a058b0c3fd22a3f41faff3969f8e09ba.gif(9)

Separating the variables

06861c9f37042cd1ac9880600c5136b1.gif(10)

Integrating

eb1052106ddf0671b3ee898bce2279c8.gif(11)

0afc28b1b4e13dbe09c308d107327207.gif(12)

Substituting (12) in equation (10)

405d0e82aab0e4cb688a90b92a0dab77.gifI can suugest you also to visit this site for more examples http://www.codecogs.com/reference/maths/differential_equations/homogeneous_differential_equations.php

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1 Answer

2x -y +z -w = -1 x +3y -2z = -5 3x -2y +4w = 1 -x +y -3z -w = -6 solve for the variables w,x,y,z using matrix equation


You have to put the equations into matrix form first. To do this, each variable has one column in the first matrix and you fill in the co-efficients for the variables. The second matrix has one column and contains all the numbers.

{ 2 -1 1 -1} = Matrix A
{ 1 3 -2 0}
{ 3 -2 0 4}
{-1 -3 -3 -1}

{-1} = Matrix B
{-5}
{ 1}
{-6}

{x=-2} = A*(B^-1)
{y=-.2}
{z=3}
{w=1/6}

I used excel for all my calculation and a helpful tutorial can be found here. I hope this helps and have a nice day!

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289818e.jpg
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7x-2y=1 y=3x


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