# Thread: [SOLVED] Calculus differential equation

1. ## [SOLVED] Calculus differential equation

Solve the following differential equations

a) dy/dx = 24x(3x^2+9)^2

b) dy/dx = 2sin(3x+infinity) infinity is a constant

I have done question a and come up with 216x^5+1296x^3+1944x

I don't know if this is right.

Please give me some tips on how to do these.

Cheers

2. Originally Posted by jet2479
Solve the following differential equations

a) dy/dx = 24x(3x^2+9)^2
these are among the easiest types of differential equations you will get. just integrate both sides.

$\displaystyle \frac {dy}{dx} = 24x \left( 3x^2 + 9 \right)^2$

$\displaystyle \Rightarrow y = 24 \int \left( 3x^2 + 9 \right)^2~dx$

We proceed by substitution.

Let $\displaystyle u = 3x^2 + 9$

$\displaystyle \Rightarrow du = 6x ~dx$

$\displaystyle \Rightarrow \frac {1}{6}~du = dx$

So we have:

$\displaystyle y = \frac {24}{6} \int u^2 ~du$

$\displaystyle \Rightarrow y = \frac {4}{3} u^3 + C$

$\displaystyle \Rightarrow y = \frac {4}{3} \left( 3x^2 + 9 \right)^3 + C$

b) dy/dx = 2sin(3x+infinity) infinity is a constant
"infinity is a constant," now there's a thought!

same story here, integrate both sides. you try this one