Find y in terms of x for the equation 2x(dy/dx) + 4y = 8x^2
divide through by 2x to get: dy/dx + 2y/x = 4x this is now in the form of dy/dx + P(x)y = Q(x)
intergrating factor = exp( integral(P(x)) dx ) = exp( integral(2/x) dx ) = exp( 2 ln(x) ) = x2
therefore d( (x2)y )/dx = 4 x3 -> (x2)y = integral ( 4x^3 ) dx = x4
therefore y = x2
TE
Answered by Tom E. • Further Mathematics tutor
7800 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸By using an integrating factor, solve the differential equation dy/dx + 4y/x = 6x^-3 (6 marks)
'Find the first derivative, with respect to x, of arctan(1/x) for non-zero real x. Hence show that the value of arctan(x)+arctan(1/x) is constant for all non-zero x, explicitly stating this constant in your final answer.' How do I solve this?
Find the square root of i
z = 4 /(1+ i) Find, in the form a + i b where a, b belong to R, (a) z, (b) z^2. Given that z is a complex root of the quadratic equation x^2 + px + q = 0, where p and q are real integers, (c) find the value of p and the value of q.