Find the integral of ((2(7x^(2)-xe^(-2x))-5)/x) . Given that y=27 at x=1, solve the differential equation dy/dx=((2(7x^(2)-xe^(-2x))-5)/-3x).y^(2/3) in terms of y.

Part A)Expand numerator in the integral to get 14x^(2) - 2xe^(-2x)-5Now divide by denominator to get 14x - 2e^(-2x) - 5/xNow integrate to get 7x^(2) + e^(-2x) - 5ln(x)Part B)Get all components of y on the left, and all components of x on the right to get -3⌠ y^(-2/3) dy = ⌠ ((2(7x^(2)-xe^(-2x))-5)/x) dx ⌡ ⌡ 3. solve to get -9y^(1/3) = 7x^(2) + e^(-2x) - 5ln(x) + C 4. Now substitute given values of x and y (1 and 27 respectively), in order to calculate C -27 = 7 + e^(-2) - 0 + c C = -34-e^(-2) 5. Substituting in C we get -9y^(1/3) = 7x^(2) + e^(-2x) - 5ln(x) + (-34-e^(-2)) 6. Rearranging in terms of y we get y = (-1/729).(7x^(2) + e^(-2x) - 5ln(x) - 34 - e^(-2))^(3)

Answered by George R. Maths tutor

3880 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate with respect to x: y=(6x^2-1)/2sqrt(x)


(a) Express 9x+11/(2x+3)(x-1) as partial fractions and (b) find the integral of 9x+11/(2x+3)(x-1) with respect to x


Given an integral of a function parametrized with respect to an integer index n, prove a given recursive identity and use this to evaluate the integral for a specific value of n.


How do you differentiate the curve y = 4x^2 + 7x + 1? And how do you find the gradient of this curve?


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