Answered

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[tex]y' - x^{4} + 3x^{2} +6 = 0[/tex]

Sagot :

Trancescient

Step-by-step explanation:

Let's rewrite y' as differential and put everything else on the right hand side:

[tex]\dfrac{dy}{dx} = x^4 - 3x^2 - 6[/tex]

Multiplying both sides by dx, we get

[tex]dy = x^4dx - 3x^2dx - 6dx[/tex]

Integrating this, we get

[tex]\displaystyle y = \int{x^4dx} - 3\int{x^2dx} - 6\int{dx}[/tex]

or

[tex]y = \frac{1}{5}x^5 - x^3 -6x + C[/tex]

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