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
7929 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Find the general solution to the differential equation y'' + 4y' + 3y = 6e^(2x) [where y' is dy/dx and y'' is d^2 y/ dx^2]
A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0. Find dy/dx and d^2y/dx^2. Verify that C has a stationary point when x = 4
Find the square roots of 2 + isqrt(5)
A particle is moving in a straight line with simple harmonic motion. The period of the motion is (3pi/5)seconds and the amplitude is 0.4metres. Calculate the maximum speed of the particle.