y' + (3/x ) = x-1  , y

Nur Hidayah

Nur Hidayah

Answered question

2022-06-03

y' + (3/x ) = x-1  , y = x^2 /5 - x/4 + 2/x^3

 

Answer & Explanation

karton

karton

Expert2023-05-19Added 613 answers

To solve the first-order linear ordinary differential equation:
y+3x=x1
Given that y=x25x4+2x3, we can begin by differentiating y with respect to x to find y:
y=ddx(x25x4+2x3)
Differentiating each term separately, we have:
y=2x5146x4
Now, let's substitute y and y back into the original equation:
(2x5146x4)+3x=x1
Combining like terms and simplifying, we get:
2x5146x4+3x=x1
To eliminate fractions, we can multiply the entire equation by the common denominator 20x4:
8x55x448+60x=20x520x420x3
Rearranging the terms, we have:
12x515x4+20x360x+48=0
At this point, the equation does not appear to simplify further, and we have obtained an algebraic equation. To solve for x, we can use numerical methods or approximations.
Therefore, the solution to the given differential equation is the set of x values that satisfy the equation 12x515x4+20x360x+48=0.

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