# Thread: First Order Linear Differential Equation

1. ## First Order Linear Differential Equation

I was having a problem trying to identify the P(x) and q(x) of this question,

(X^3)d/dx(y(x))-(4X^2)y(x)=(4x^7)

I would be really thankful if someone could help me with this!

Thanks!

2. Originally Posted by anthony162
(X^3)d/dx(y(x))-(4X^2)y(x)=(4x^7)

Dividing $x^3y'-4x^2y=4x^7$ by $x^3$ we get $y'-(4/x)y=4x^4$ .

So, $p(x)=-4/x,\;q(x)=4x^4$ .

3. Thanks alot i've just found out that i had mistaken that the y(x) is part of another equation,thanks for your help!

4. All right, take into account that

$\dfrac{d}{dx}\;(y(x)):=y'(x)$

5. The equation is also Cauchy-Euler.