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

6818 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

A particle is launched from the top of a cliff of height 87.5m at time t=0 with initial velocity 14m/s at 30 deg above the horizontal, Calculate: a) maximum height reached above bottom of cliff; b)horizontal distance travelled before hitting the ground.


Expand (1+x)^3. Express (1+i)^3 in the form a+bi. Hence, or otherwise, verify that x = 1+i satisfies the equation: x^3+2*x-4i = 0.


How do you calculate the derivative of cos inverse x?


A block of mass 50kg resting on a rough surface with a coefficient of friction equal to 1/3. Find the maximum angle at which the surface can be inclined to the horizontal without the block slipping. Give your answer to 3 significant figures


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences