- Forums
###### Differential Equation

watch this thread

2 weeks ago

Bit stuck on how to get the answer for exercise 3. Attached photo with my working. I’ve kind of got what I’m supposed to but don’t know how to get rid of the cos function so that I’m just left with the sine function.

And for exercise 4, would I just differentiate, set to 0 and then go from there?

And for exercise 4, would I just differentiate, set to 0 and then go from there?

Original post by vc94

In ex.3, in your solution for y, aren't you missing some arbitrary constants?

In ex.4, isn't terminal velocity achieved when t tends to infinity?

In ex.4, isn't terminal velocity achieved when t tends to infinity?

Would it just be A and B in front of cos and sin respectively? Idk how to go from there to the solution they want.

I thought it would be when acceleration = 0 but I’m probably wrong.

Original post by kwikmaffs

Would it just be A and B in front of cos and sin respectively? Idk how to go from there to the solution they want.

I thought it would be when acceleration = 0 but I’m probably wrong.

I thought it would be when acceleration = 0 but I’m probably wrong.

Yes for A and B. The question asks for a/one solution, not the general solution so what (obvious) values for A and B would give what they want?

Terminal velocity would have dv/dt = 0, though as its name suggests that it would be the "terminal" value so as t -> inf? If you sketch the velocity curve / do some very simple reasoning about the fraction it should be clear (rather than doing calculus).

Original post by mqb2766

Yes for A and B. The question asks for a/one solution, not the general solution so what (obvious) values for A and B would give what they want?

Terminal velocity would have dv/dt = 0, though as its name suggests that it would be the "terminal" value so as t -> inf? If you sketch the velocity curve / do some very simple reasoning about the fraction it should be clear (rather than doing calculus).

Terminal velocity would have dv/dt = 0, though as its name suggests that it would be the "terminal" value so as t -> inf? If you sketch the velocity curve / do some very simple reasoning about the fraction it should be clear (rather than doing calculus).

So 1/2 and then minus one from the other? Thanks! Haven’t actually done second order differential equations yet but it appeared on the homework so it threw me a bit.

Original post by kwikmaffs

So 1/2 and then minus one from the other? Thanks! Haven’t actually done second order differential equations yet but it appeared on the homework so it threw me a bit.

If its

y ~ Asin + Bcos

then its just A=1, B=0?

Original post by mqb2766

If its

y ~ Asin + Bcos

then its just A=1, B=0?

y ~ Asin + Bcos

then its just A=1, B=0?

Oh yeah that works, sorry I watched a YouTube video where they added and minused 1 equations and multiplied by 1/2. Thanks

Original post by kwikmaffs

Oh yeah that works, sorry I watched a YouTube video where they added and minused 1 equations and multiplied by 1/2. Thanks

If the question had said "verify", it would simply have wanted you to substitute it into the ODE and verify the LHS was zero. If youre a bit unsure/rusty/... Its not a bad short exercise (rather than watching youtube) to verify that both

y = e^(-2mt)sin(4mt)

y = e^(-2mt)cos(4mt)

are solutions to the ODE, then deduce why

y = Ae^(-2mt)sin(4mt)y + Be^(-2mt)cos(4mt)

is also a (the general) solution to the linear ODE.

(edited 2 weeks ago)

- What to cover in a differential equations module?
- differential equations
- Stationary points
- Where to find more of these questions? / What is the name of this topic?
- Help differentiation
- Differential equations
- URGENT as level maths question help needed
- isaac physics 7.6.1. Circular Motion
- UCAS Clearing 2023 FAQ and Help Megathread
- Got a Ucas or results related question? Ask a Clearing and Applications Advisor here
- Differentiation help
- AS OCR differentiation help please
- maths question help
- A Level maths past paper question help needed
- a =w2x prove it pls
- Need help with maths
- Help! Maths A level advice
- Maths a level
- Imperial MSc mathematics and finance
- Physics

- GCSE Mathematics Study Group 2023-2024
- Hypothesis Testing
- Step support programme assignment 7 help pls
- Senior Maths Challenge 2023
- A-level Mathematics Study Group 2023-2024
- Dimensional Analysis
- Do we have to memorise all physics equations for GCSE 2024 ?
- Girls Maths Olympiad 2023
- Electrical Engineering maths help with Desmos graphing calculator
- A Level Maths Moments question
- Discrete maths questions
- Plotting data on a graph.
- Hypothesis Testing
- Problem solving the smc 2023
- Maths trig
- Help With A level Trig
- which calculator; the fx-991cw or fx-991ex
- AS Maths edexcel 2023
- Edexcel AS Stats and mechanics paper 2023?
- Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrong

- Official Veterinary Medicine Applicants thread 2024 entry
- Deloitte Graduate Scheme 2024
- DWP Work Coach - Reserve List July 2023
- crush
- is it selfish of me
- ATAS certificate for UK for January 2024 intake
- should i get rejected to move on?
- DWP Work Coach Interview - how long to hear
- HO Customer Service Group EO - National - 315941 Interview Extension
- Customer Services Group (EO) - 315941

- Home Office - Asylum Decision Maker (EO)
- JP Morgan Tech Connect 2023
- LearnDirect Access Course - Engineering
- Getting into QMUL with an access course
- Anyone gotten into uni with an access course ? & which one ?
- Monarchists vs Republicans
- [Official thread] Hamas-Israel Conflict
- Cambridge Interview
- 2024 entry A100 / A101 Medicine fastest and slowest offer senders
- Ucas account used again

- KU Top Tips – How To Prepare The Day Before A Big Uni Exam
- Aston University computer science
- Official Thread: (Undergraduate) Medicine 2024 Entry
- Official: Queen's University Belfast A100 2024 Entry Applicants
- Last Person To Post Here Wins (Part 54)
- personal statement
- Bristol medicine on hold 2024 entry
- Girls Vs. Boys (Part 45)
- Official Thread: Graduate Entry Medicine 2024 Entry
- Could I quit my work to do this

- how do will spy on a cheating partner
- The Official Cambridge Applicants for 2024 Entry Thread
- Official: University of Cambridge A101 Applicant and Offer Holder thread 2023 Entry
- Lloyds Graduate Scheme 2023
- Law offers - 2024 entry
- The Arsenal Thread XXVI
- KU Students: Check out The Career Centre!
- University of Warwick medicine 2024 Entry
- What do people wear at a Cambridge interview?
- Can I evict myself from halls

The Student Room and The Uni Guide are both part of The Student Room Group.

© Copyright The Student Room 2023 all rights reserved

The Student Room and The Uni Guide are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: Imperial House, 2nd Floor, 40-42 Queens Road, Brighton, East Sussex, BN1 3XB