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Solve the differential equation dy/dx = y/x(x + 1) , given that when x = 1, y = 1. Your answer should express y explicitly in terms of x.

Rearrange differential equation to get 1/x(x+1) dx = 1/y dy. Separate x side into partial fractions where 1/x(x+1) = 1/x - 1/(x+1). Integrate each side. Resulting equation involves natural logs. Substitut...

Answered by Alexander T. • Maths tutor

16845 Views

The expansion of (1+x)^4 is 1 + 4x +nx^2 + 4x^3 + x^4. Find the value of n. Hence Find the integral of (1+√y)^4 between the values 1 and 0 (one top, zero bottom).

Using Binomial expansion or Pascal's triangle, expand (1+x)^4 to get 1+4x+6x^2+4x^3+x^4. Then, by substituting √y for x, get 1 + 4y^1/2 + 6y +4y^3/2 +y^2. Then, using the rules of integration, the expansi...

Answered by Tutor41123 D. • Maths tutor

6567 Views

Factorise y^2 + 7y + 6

So here we have a quadratic equation because it has the structure a^2 + bx + c. In order to factorise a quadratic we first need to look for two numbers that we can multiply together to get 6 and add toget...

Answered by Victoria H. • Maths tutor

13914 Views

Express 4 sin(x) – 8 cos(x) in the form R sin(x-a), where R and a are constants, R >0 and 0< a< π/2

4 sin(x) – 8 cos(x)= Rsin(x-a) here use double angle formula

4 sin(x) – 8 cos(x)= Rsin(x)cos(a)-Rcos(x)sin(a) Rearrange so in same format as LHS

4 sin(x) – 8 cos(x)= Rcos(a)sin(x)-Rsin(a)cos...

Answered by Simon E. • Maths tutor

24516 Views

Point A (-3,5) and point B (1,-15) are to be connected to form a straight line, fing the equation of the line in the form y=mx+c?

First identify your x1, y1 and x2,y2. It is helpful to write this above the two points A and B. To find the gradient the following equation can be used (I will show equation on board),as u can see the X1,...

Answered by Charuka W. • Maths tutor

5890 Views