Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
The solution to the given differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex] is , [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
For given question,
We have been given a differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex]
We know that for any real number a, m, n,
[tex]a^{m + n} = a^m \times a^n[/tex]
⇒ dy/dx = [tex]e^{4x}[/tex] × [tex]e^{5y}[/tex]
Separating the variables (x and its differential in one side and y and its differential in another side )
⇒ [tex]\frac{1}{e^{5y}}[/tex] dy = [tex]e^{4x}[/tex] dx
⇒ [tex]e^{-5y}[/tex] dy = [tex]e^{4x}[/tex] dx
Integrating on both the sides,
⇒ [tex]\int e^{-5y}[/tex] dy = [tex]\int e^{4x}[/tex] dx
We know that, [tex]\int e^{ax}\, dx=\frac{e^{ax}}{a} +C[/tex]
⇒ [tex]\int e^{4x}\, dx=\frac{e^{4x}}{4} +C[/tex]
and [tex]\int e^{-5y}\, dy=\frac{e^{-5y}}{-5} +C[/tex]
So the solution is, [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
Therefore, the solution to the given differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex] is , [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
Learn more about the differential equation here:
https://brainly.com/question/14620493
#SPJ4
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
