Give the general solution to (d2y/dx2) - 2dy/dx -3y = 2sinx
Using the auxiliary equation t^2 - 2t - 3t = 0 t therefore is equal to 3 or -1. Using this value, a complementary function is derived. Y= Ae^(3x) + Be^(-x). Finally, to fully solve, a particular integral of y = asinx + bcosx and differentiate it twice, to give equations for Dy/dx and (d2y/dx2). These can be substituted into the initial differential equations to find the values of a and b, Which are -2/5 and 1/5 respectively. The answer is then the complementary function plus the solution to the particular integral y = Ae^(3x) + Be^(-x) + (1/5)cosx - (2/5)sinx
BY
Answered by Bradley Y. • Further Mathematics tutor
10223 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)
Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.
What is the value of x from (x+2)^2=4
How far is the point (7,4,1) from the line that passes through the points (6,4,1) and (6,3,-1)?