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JinKazama1
@JinKazama1
September 2021
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Please Annswer Q:5
Solve above Differential Equation :
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Swarup1998
Verified answer
The answer is given in the attachment.
Thank you for your question.
2 votes
Thanks 8
Nikki57
Thanks ^_°
Yuichiro13
Verified answer
_____________________________________________________________
♦ Ordinary Differential Equations ♦
◙ Bernoulli ODE ◙
→ First Order Bernoulli ODE has the form : y' + p( x )y = q( x )yⁿ
• p( x ) and q( x ) are continuous functions and n ∈ R
→ Solving Bernoulli involves subtituting v = y¹⁻ⁿ , so we use that in our solution.
_____________________________________________________________
→ THE ATTACHMENT TO BE REFERRED :
• General Solution for the First Order Linear ODE is given by :
→ where p( x ), q( x ) have their usual representation when the ODE is written in the simplest form.
__________________________________________________________
→ Just work up with the Algebra and you get : C = 0
____________________________________________________________
♦Result :
____________________________________________________________
→ For further details on Bernoulli ODE's : ♦ http://tutorial.math.lamar.edu/Classes/DE/Bernoulli.aspx
• The website above mentioned 0_0 gives an insight into all sorts of ODE's and their generalized Problem Solving Methods
♦ http://mathworld.wolfram.com/BernoulliDifferentialEquation.html
_____________________________________________________________
^_^ Hope it helps !
3 votes
Thanks 9
Nikki57
Thanks !
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Answers & Comments
Verified answer
The answer is given in the attachment.Thank you for your question.
Verified answer
_____________________________________________________________♦ Ordinary Differential Equations ♦
◙ Bernoulli ODE ◙
→ First Order Bernoulli ODE has the form : y' + p( x )y = q( x )yⁿ
• p( x ) and q( x ) are continuous functions and n ∈ R
→ Solving Bernoulli involves subtituting v = y¹⁻ⁿ , so we use that in our solution.
_____________________________________________________________
→ THE ATTACHMENT TO BE REFERRED :
• General Solution for the First Order Linear ODE is given by :
→ where p( x ), q( x ) have their usual representation when the ODE is written in the simplest form.
__________________________________________________________
→ Just work up with the Algebra and you get : C = 0
____________________________________________________________
♦Result :
____________________________________________________________
→ For further details on Bernoulli ODE's : ♦ http://tutorial.math.lamar.edu/Classes/DE/Bernoulli.aspx
• The website above mentioned 0_0 gives an insight into all sorts of ODE's and their generalized Problem Solving Methods
♦ http://mathworld.wolfram.com/BernoulliDifferentialEquation.html
_____________________________________________________________
^_^ Hope it helps !