is the first thing used to find the constant? and the 2nd says put x as 2?

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33 Replies
iTeachChem Helper
@Apu
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Opt
Opt2mo ago
So, you get y as some function of x with a arbitrary constant right?
burrito
burritoOP2mo ago
yes
Opt
Opt2mo ago
The y(1)=1 specifies a specific function in that family of function so that you get a value for the constant of integration C It's called an initial condition
burrito
burritoOP2mo ago
ohhhhhhhh ahh sothey give uthe initial condition for C
Opt
Opt2mo ago
Once you find the specific function by plugging in x=1 and equating the expression to 1, you can input x=2 to get the final answer. Yup The more the number of arbitrary constants, the more the number of initial conditions required.
burrito
burritoOP2mo ago
i see thank you
Opt
Opt2mo ago
The equation looks separable so it's easy enough.
burrito
burritoOP2mo ago
yes
Opt
Opt2mo ago
Got it?
burrito
burritoOP2mo ago
yes
burrito
burritoOP2mo ago
@Opt whats ths thing for identifying homogenous eqn
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burrito
burritoOP2mo ago
like he said on top its 1+1 and bottom its 2 so shuld top and bottom have same power
Opt
Opt2mo ago
Do the simple thing just and just substitute x by kx and y by ky on the RHS If all the k's cancel out, it's homogeneous Yeah that's the same thing.
burrito
burritoOP2mo ago
ahh
Opt
Opt2mo ago
deg(numerator) = deg(denominator)
burrito
burritoOP2mo ago
ohhh i might be asking a gazillion doubts for 1 week (maths board)
Opt
Opt2mo ago
It's fine.
burrito
burritoOP2mo ago
wait
burrito
burritoOP2mo ago
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burrito
burritoOP2mo ago
if i take anti log in 1st step ill get a diff answer no? wait can u take anti log thru addition i think u cant
burrito
burritoOP2mo ago
@CertifiedBrownMunda arent both these lines y=x?
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CertifiedBrownMunda
Nope. Red one will be y=x (assuming slope is 1) and blue one will be y=-x (assuming slope is -1)
burrito
burritoOP2mo ago
ohho righttt wait it lies in -x axis plane is that why?
CertifiedBrownMunda
not really. It has to do with the slope of the line. Are you comfortable with trigonometry @burrito ?
burrito
burritoOP2mo ago
uh yea sure lemme see
CertifiedBrownMunda
So the red line will probably make an angle between 0 and 90 with positive x-axis. Slope will be tan of this angle. For y=x the angle should be 45 degrees For y=-x, the angle will be 135. Tan135 is negative
burrito
burritoOP2mo ago
ohhhhh rightt makess sense thank you
CertifiedBrownMunda
No worries. No doubts are dumb doubts. Just put it in the doubts channel. Someone, if not me, will come to rescue. Happy learning
burrito
burritoOP2mo ago
🙏🙏okay
iTeachChem
iTeachChem2mo ago
yea please ask one doubt on a thread, and better to ping the doubt solver thing than ping folks directly :) +solved @Opt
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