Question

find the derivative by removing arbitrary constant A and B , y=Ax³+Bx².

Answer 1

Hey there !!!!!

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y=Ax³+Bx²----Equation 1

Differentiating equation 1 wrt "x"

dy/dx = 3Ax²+2Bx

y₁ = 3Ax²+2Bx----Equation 2

Further differentiating 

d²y/dx² =6Ax+2B

y₂=6Ax+2B----Equation 3


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y=Ax³+Bx²----Equation 1

Multiplying Equation 1 with "two"

2y=2Ax³+2Bx²----Equation 4

y₁ = 3Ax²+2Bx----Equation 2

Multiplying equation 2 with "x" 

y₁x = 3Ax³+2Bx²----Equation 5

Now Subtracting Equation 4 and Equation 5

y₁x-2y= Ax³

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y₁ = 3Ax²+2Bx----Equation 2 

Multiplying equation 2 with "2x"

2y₁x = 6Ax³+4Bx²----Equation 6

y₂=6Ax+2B----Equation 3

Multiplying equation 3 with "x²"

y₂x²=6Ax³+2Bx²----Equation 7

Subtracting equation 6 & 7

2y₁x-y₂x²=2Bx²    y₁x-2y= Ax³

y=Ax³+Bx²

y=(y₁x-2y) - (2y₁x-y₂x²)/2

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Hope this helped you..............