1st order differential eqn raised to power of 1.7

[karthikphenom]

Homework Statement

This is the eqn I need to solve:
(dy/dx)^1.7 = c

Homework Equations

The Attempt at a Solution

1) 1.7ln(dy/dx) = c [since 'c' is an arbitrary constant, I'm writing ln(c) as 'c' itself]

2)ln(dy/dx) = c/1.7

3)dy/dx = e^(c/1.7)

4)y = xe^(c/1.7)

Now, the above solution says that y is a linear function of x. The solution is similar to what we obtain for "dy/dx = c", i.e. another linear solution. So I'm beginning to wonder whether what I did was correct. Can anyone help?

 

[Prologue]

You could just take the 1.7th root of the equation to get this

$$\frac{dy}{dx}=c^{\frac{1}{1.7}}$$

$$\frac{dy}{dx}=c'$$

Where c' is just another constant.

So in other words, it is just a linear function.

 

[karthikphenom]

Thanks for the reply Prologue. So if this is a linear function too, then what exactly is the difference between the solution for "dy/dx = c" and "(dy/dx)^1.7 = c" besides the actual numerical value of dy/dx?

 

[Prologue]

In differential equation terms...nothing. They have the same solution,

y = (arbitrary constant)x + (arbitrary constant)

 

[karthikphenom]

Cool.. Thanks again...