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Solve the differential equation dy/dx=(y^(1/2))*sin(x/2) to find y in terms of x.

Here, we must first rearrange our equation so all x terms are on one side and all y terms are on the other. Multiplying both sides by dx and diving both by y^(1/2) gives us y^(-1/2)dy = sin(x/2)dx, which is ...
AJ
Answered by Alex J. • Maths tutor
7681 Views

Expand and simplify (x+4)(x-5).

For this, we use the FOIL method of expanding brackets; start by multiplying the FIRST terms of each bracket together to get x x=x^2. Next multiply the OUTSIDE elements, ie the first element in the first bra...
AJ
Answered by Alex J. • Maths tutor
30603 Views

Find the first differential with respect to x of y=tan(x)

To answer, we must be familiar with several trigonometric identities and expressions; first notice that tan(x)=sin(x)/cos(x). Now our function is a quotient of two functions of x that we can easily different...
AJ
Answered by Alex J. • Maths tutor
8413 Views

Solve the simultaneous equations: y=2x+2, y=x^2 - 1

The solution to this question can be obtained algebraically using substitution. As both equations are equal to y, this also means they are equal to each other. So firstly, substitute the simpler equation whi...
SN
Answered by Sahil N. • Maths tutor
14672 Views

Why is it that when I am asked to factorise 3x^2-13x-10, I am not able to cancel two of the x's so that the answer is 3x-13-10?

This is because to be able to cancel an 'x' in the equation the 'x' needs to be multiplying every constant. For example, if you were to think of the 'x' as equaling 3 in the question above, then the 10 would...
VW
Answered by Victoria W. • Maths tutor
4662 Views