The solution to the given differential equation
is ,
, where c is constant of integration.
For given question,
We have been given a differential equation ![\frac{dy}{dx} = e^{4x+5y}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20e%5E%7B4x%2B5y%7D)
We know that for any real number a, m, n,
![a^{m + n} = a^m \times a^n](https://tex.z-dn.net/?f=a%5E%7Bm%20%2B%20n%7D%20%3D%20a%5Em%20%5Ctimes%20a%5En)
⇒ dy/dx =
× ![e^{5y}](https://tex.z-dn.net/?f=e%5E%7B5y%7D)
Separating the variables (x and its differential in one side and y and its differential in another side )
⇒
dy =
dx
⇒
dy =
dx
Integrating on both the sides,
⇒
dy =
dx
We know that, ![\int e^{ax}\, dx=\frac{e^{ax}}{a} +C](https://tex.z-dn.net/?f=%5Cint%20e%5E%7Bax%7D%5C%2C%20dx%3D%5Cfrac%7Be%5E%7Bax%7D%7D%7Ba%7D%20%2BC)
⇒
and ![\int e^{-5y}\, dy=\frac{e^{-5y}}{-5} +C](https://tex.z-dn.net/?f=%5Cint%20e%5E%7B-5y%7D%5C%2C%20dy%3D%5Cfrac%7Be%5E%7B-5y%7D%7D%7B-5%7D%20%2BC)
So the solution is,
, where c is constant of integration.
Therefore, the solution to the given differential equation
is ,
, where c is constant of integration.
Learn more about the differential equation here:
brainly.com/question/14620493
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<span>S= (a+b)^2+(4a+b-2)^2+(9a+b-4)^2
98a+14b-44=0
14a+3b-6=0
a=24/49, b=-2/7
y = (24/49)x^2-(2/7)</span>
Answer:
The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2
I dont know the exact positions to put the lengths, but tell me if this helps!