Question

Solve the ODE
\[\frac{\text dy}{\text dx}=\frac{2y-x-1}{4x-3y-6}\]

Answer 1

i got \[(3y+x-9)^5=A(y-x+1)\]
how can i check it?

Answer 2

where A is a constant

Answer 3

so to check if it is a solution to the Differential Equation, we differentiate right?
and hopeful get back the original DE,

Answer 4

my working

Answer 5

???

Answer 6

also if you can show me a was to solve the DE that dosent take three pages that would be helpful too

Answer 7

Well your solution seems perfectly alright to me - I went through it step by step, and it seems okay - except where you differentiate it - am not sure if that's okay too (the last too steps).


This problem can be shortened (according to my knowledge) only at the point where you have used partial fractions - instead of that why dont you make a whole square in the denominator, and then split the numerator?

Answer 8

**two steps

Answer 9

sorry unkle.. anything with more 1/2 a page of work i start seeing pink elephants...

Answer 10

this is just a single problem from a set of 12
i have been working on the set all year

Answer 11

This is that last one

Answer 12

Unkle can you make whole square of the rm instead of using partial fractions??

Answer 13

i am not sure how to do that
do you mean after this step?\[\frac{\text dX}{X}=\frac{4-3V}{3V^2-2V-1}\text dV\]

Answer 14

yes.

Answer 15

\frac{\text dX}{X}=\frac{4-3V}{3V^2-2V-1}\text dV

Answer 16

You know what - what you did was the best possible method actually - creating whole squares is pretty tedious in the current arrangement of numbers. - I guess this is the only way you'll have to proceed in this question.

Answer 17

i am not sure what the whole square method is
is the same as completing the square?
can you provide a simple example