Calculate y as a function of x when dy/dx = 4x3 + 3x2 - 6x + 5 a. x4 + x3 - 3x2 + 5x + c b. 12x2 +3x + c c. 4x4/3 + x3 - 6x2 + 5x + c d. 4x2 +3x + c

y = x⁴ + x³ - 3x² + 5x + C

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Separable differential equations such as these ones can be solved by treating dy/dx as a ratio of differentials. Then move the dx with all the x terms and move the dy with all the y terms. After that, integrate both sides of the equation.

   

In general (understood that +C portions are still there), 

   

Note that ∫dy = y  since it is ∫1·dy = ∫y⁰ dy = y¹/(0+1) = y
For the right-hand side, we use the sum/difference rule for integrals, which says that

   

Applying these concepts:

   

The answer is y = x⁴ + x³ - 3x² + 5x + C

M< 5 = 80 , < 2 = 80, < 6= 100, < 3= 100, < 7= 80, < 4= 80, < 8= 100

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