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Form the differential equation representing the family of curves x = my , where, m is arbitrary constant.

Differentiating the above equation with respet to y:dx/dy = m;Substituting the value of m in the given form:x = (dx/dy) y i.e. the solution is(dx/dy) y - x = 0
PS
Answered by Piyush S. • Maths tutor
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Find the positive value of x such that log (x) 64 = 2

Find the positive value of x such that log x 64 = 2 Using the logarithm rules, we know that we can rearrange the given equation into the form: x 2 = 64 Knowing this, we square root both sides to get x = 8, x...
SG
Answered by Santiago G. • Maths tutor
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Show that the equation 5sin(x) = 1 + 2 [cos(x)]^2 can be written in the form 2[sin(x)]^2 + 5 sin(x)-3=0

First, we need to realise that we will be using the trigonometric identity sin(x) 2 + cos(x) 2 = 1 As our goal is to end up with an equation involving only sin, we will therefore substitue cos(x) 2 with ( 1 ...
SG
Answered by Santiago G. • Maths tutor
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Integrate the function : F'(x)=3x^2+4x-5

F'(x)=3x^2+4x-5 F(x)=(3/(2+1))(x^(2+1))+(4/(1+1)) (x^(1+1))-5(x^(0+1)) Answer: F(x)=x^3+2x^2-5x+c
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Answered by Ian Malique D. • Maths tutor
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What exactly IS differentiation?

This is a common question as we are often taught to differentiate by simply being told how to do the calculation, but not what it is we're really doing. The concept Differentiation is finding the gradient of...
JH
Answered by John H. • Maths tutor
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