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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. Substitute i...
AT
Answered by Alexander T. • Maths tutor
17608 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 expansion ...
TD
Answered by Tutor41123 D. • Maths tutor
7136 Views

Why was the bay of pigs incident such a major setback for the United States and for President Kennedy?

When Kennedy came into power in January 1961 he made a famous speech in which he said they would fight anyone to 'assure the survival and success of liberty'. By 1961 Fidel Castro was firmly on the side of t...
JL
Answered by Jasmine L. • History tutor
10481 Views

How can I improve my essays in order to get the top band of marks, my feedback says need more analysis and explanation?

In order to move to the top band of marks, it is important to not just describe and explain, but to give your own point of view on the issue. Giving your judgement is the key to getting the top marks. After ...
PE
Answered by Pascal E. • History tutor
2592 Views

When should we use the subjunctive tense in Spanish?

In English, less and less people use the subjunctive, so it can be hard for us to recognise when it is needed in Spanish. However, we can generally follow this rule: when there is any level of doubt or uncer...
EO
Answered by Emily O. • Spanish tutor
3252 Views