The following ODE is solved by the following function.
How do I determine the values of a, b and c?

Question

The following ODE is solved by the following function.
How do I determine the values of a, b and c?

anonymous · Answer

ODE: $$y' + ax^b \sin (x^c) y =0$$
Soluioin: $$y = e^{ \cos (x^4)}$$

anonymous · Answer

Should I do this:
Calculate y' from the solution, thus $$y' = e^{ \cos (x^4)} \times - \sin (x^4) \times 4x^3$$

Now I plug this into the ODE:
$$\color {green} a x^{\color {red} b} \sin (x^{\color {blue} c}) y =\color {green}4x^{\color {red} 3} \sin (x^{\color {blue} 4}) e^{ \cos (x^4)}$$
and get that a = 4, b = 3 c = 4?

luigi0210 · Answer

Is this calculus?

luigi0210 · Answer

Well this high school senior just got through calculus one so I won't be much help here. My apologies

anonymous · Answer

What would y' be?  I did it again and got my old answer again

anonymous · Answer

@Luigi0210 hahahaah:)

luigi0210 · Answer

I will observe and learn

anonymous · Answer

I did it right?

luigi0210 · Answer

What? oh darn it -_-

anonymous · Answer

@Loser66 cool!  I'm currently busy with Cal3 and some other subjects. next semester is cal4 (i think numberical analysis?)


Oh and sorry, but I don't see what I did wrong?

loser66 · Answer

oh, yeah, since you put - out side of sin, it confused me, Oh I am sorry. my mis read, i think you got y' = ... -(minus) .... my bad, I apology.!!

loser66 · Answer

@taljaards in my college, differential equations is a separate course after cal3.

phi · Answer

yes, I get a=4, b=3, c=4

anonymous · Answer

@Loser66 haha you confused me too haha, but nvm thanks for the help! Thanks @phi!


At ours Cal3 also isn't DE...
I have DE, Cal3, linear algebra1 and other subjects..