Solve the differential equation y'= 2x^3 + 4x - 5.

Question

irishboy123 · Answer

go for it !! and post here

prettygirl_shynice · Answer

ill help

jmartinez638 · Answer

Yeah, idk really what to do.

irishboy123 · Answer

go @Prettygirl_shynice   !!

jmartinez638 · Answer

lol

jmartinez638 · Answer

Oh no. I understand what's happening, and it is difficult

jmartinez638 · Answer

A normal seperable equation would have, for example, an x and a y, and a dx and a dy. SO, since this is y', we must find y, seperate the equations, and integrate both sides.

jmartinez638 · Answer

Sound about right?

jmartinez638 · Answer

what do you think @Prettygirl_shynice

tkhunny · Answer

Have you considered first solving the characteristic equation?

jmartinez638 · Answer

Not really. Can you explain?

tkhunny · Answer

You should not have been given this problem without knowing what a characteristic equation is.  At least SHOW the characteristic equation or we really cannot proceed.

tkhunny · Answer

Once you find the roots of the equation, you can simply write down general solutions in terms of exponentials and sine and cosine.

solomonzelman · Answer

couldn't you just integrate?

jmartinez638 · Answer

$$\frac{ x(x^3+4x-10) }{ 2 } + c$$

solomonzelman · Answer

you got that when integrating??

solomonzelman · Answer

$\large\color{#000000 }{ \displaystyle \int x^n=\frac{x^{n+1}}{n+1}\color{grey}{+C} }$

zarkon · Answer

jmartinez638's answer is correct...though it is unconventionally written

solomonzelman · Answer

oh.... -:( :)

solomonzelman · Answer

wouldn't write it like this myselft, but ...

zarkon · Answer

$$\frac{ x(x^3+4x-10) }{ 2 } + c=\frac{x^4+4x^2-10x }{ 2 } + c=\frac{x^4}{2}+2x^2-5+c$$

solomonzelman · Answer

yes, yes...

jmartinez638 · Answer

$$\frac{ x^4 }{ 2 } +2x^2 -5x + $$

jmartinez638 · Answer

Sorry, plus a constant

zarkon · Answer

left off the x

$$\frac{ x(x^3+4x-10) }{ 2 } + c=\frac{x^4+4x^2-10x }{ 2 } + c=\frac{x^4}{2}+2x^2-5x+c$$

jmartinez638 · Answer

Yeah, I 'simplified' it when I should have left it

jmartinez638 · Answer

What next? I really haven't come across this specific problem, so

irishboy123 · Answer

incroyable 


@ganeshie8

ganeshie8 · Answer

Solving a differential equation means finding a function "y" that satisfies the given equation.

y = x^4/2+2x^2-5x satisfies the given differential equation, so this is a solution. 
All the solutions are given by y = x^4/2+2x^2-5x + c

tkhunny · Answer

Whoops!  What was I thinking?