# V and x separable?

1. Feb 14, 2016

### hotjohn

1. The problem statement, all variables and given/known data
i am asked to form a differential equation using dy/dx = 1 + y + (x^2 ) + y(x^2) , but i gt stucked here , hw to proceed? as we can see , the V and x are not separable

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### 0058.jpg
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2. Feb 14, 2016

### Buzz Bloom

Hi hotjohn:

You may have a typo. You say
V and x are not separable​
but the is no "V" in the equation.

Regards,
Buzz

3. Feb 14, 2016

### hotjohn

sorry , i mean y and x . How to continue ?

4. Feb 14, 2016

### Buzz Bloom

Hi hotjohn:

If you factor the 2nd equation in your attachment, and make a substitution for y in terms of a new variable, say z, you can get a separable equation involving z and x.

Hope this helps.

Regards,
Buzz

5. Feb 14, 2016

### hotjohn

sorry , i didnt get you , can you explain further ?

6. Feb 14, 2016

### Buzz Bloom

Hi hotjohn:

dy/dx = (1+y) × (1+x2)
y = z-1

Regards,
Buzz

7. Feb 14, 2016

### hotjohn

can you expalin why there is a need to sub y = z-1 ?? and how do u knw why should sub y = z-1 ? why cant be y = z-2 ? or others ?

8. Feb 14, 2016

### Crush1986

You don't have to sub if you don't want to. Once it's separated just solve it like you would any seperable equation.

9. Feb 14, 2016

### hotjohn

how to determine the value of number or new constant to be substituted into the original equation ?

10. Feb 14, 2016

### Crush1986

Remember, unless you are given initial conditions you will have an infinite amount of answers to most differential equations.

11. Feb 15, 2016

### hotjohn

can it be y = z-2 , y = z-3 and etc ??

12. Feb 15, 2016

### Buzz Bloom

Hi hotjohn:

It is not a need, but a convenience.
y=z-1 → z=y+1 → dz/dx =z × (1+x2) →dz/z = (1+x2) dx ​
This in now the standard form for a separable equation.

Regards,
Buzz

13. Feb 15, 2016

### hotjohn

??
i found that if substituition of y=z-1 is not used , the whole equation become inseparable ...........

how do we know that y must be replaced with y=z-1 ?

14. Feb 15, 2016

### Buzz Bloom

Hi hotjohn:

As I said previously, using y = z-1 is not a necessity, and not something that must be done. I thought that making that substitution might help you see the separability more easily.

Can you complete the solution of the problem from
dy/dx = (1+y) × (1+x2) ?​

If so, you are done.

Regards,
Buzz