Find the curve whose gradient is given by dy/dx=xy and which passes through the point (0,3)

First "Separate the Variables" by rearranging the equation to get the ys on the LHS and the xs on the RHS:

(1/y) dy=x dx

Now Integrate:

Integral(1/y) dy = Integral(x) dx

ln(y)=x2/2 + constant of integration (c)

Rearrange to get y=:

e(lny)=e(x2/2)+c

y=e(x^2/2)+c = e* ex^2/2 = Ae0.5x^2

This is your GENERAL SOLUTION (GS)

Now plug in the coordinates:

3=Ae0.50=A1=A

A=3

So:

y=3e0.5x^2

This is the PARTICUAR SOLUTION (PS) and also the answer to original question

CC
Answered by Christian C. Maths tutor

3387 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I find the turning points of a curve?


Mechanics (M1): Particle moving on a straight line with constant acceleration (Relationships of the 5 Key Formulae)


State the conditions under which a binomial distribution can be approximated as a normal distribution, and state how the parameters needed would be calculated.


a) Differentiate and b) integrate f(x)=xcos(2x) with respect to x


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences