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A level Maths: Differential Equations Question

differential equation with second derivative.JPGHello, not sure how to begin solving this as I have only come across differential equations with dy/dx and not the second derivative. Any advice would be appreciated, especially worked solutions. Thanks!
Reply 1
Just use the (y=...) and differentiate and sub into the differential equation. Solve for lambda here

It’s called a second order homogeneous differential equation, but I thought it was further maths only so that’s weird
Original post by timif1
Just use the (y=...) and differentiate and sub into the differential equation. Solve for lambda here

It’s called a second order homogeneous differential equation, but I thought it was further maths only so that’s weird

Yeah I didn't see it in my A level maths textbook so I posted here haha
Thanks timif!
Reply 3
Are you sure this is covered in your course, this is further maths only in edexcel.
If you still need help with it that then look at this
Ok so you solve it as follows. IMG_20190325_192507[13644].jpg
Original post by splitter2017
Ok so you solve it as follows. IMG_20190325_192507[13644].jpg

Thanks so much splitter, extremely clear and helpful!Just what I needed!
Original post by Mshabana
Are you sure this is covered in your course, this is further maths only in edexcel.
If you still need help with it that then look at this

Thanks for that Mshabana. I haven't seen this in the single maths A level textbook but it appeared in one of the mixed exercise sections, but wasn't labelled as an extension or anything. Wanted to make sure I knew how to do it anyway
Reply 7
01E06457-3B48-49FF-87A3-C4BEE6DD651D.jpeg
This is how I solved this. The -or- part is where I reached a dead end, ignore that. But splitter2017’s post I think is wrong. Second derivative of e^λχ is not λ^2 x e^λχ, but how I wrote it. I think.
Original post by Tatsien
01E06457-3B48-49FF-87A3-C4BEE6DD651D.jpeg
This is how I solved this. The -or- part is where I reached a dead end, ignore that. But splitter2017’s post I think is wrong. Second derivative of e^λχ is not λ^2 x e^λχ, but how I wrote it. I think.

The 2nd derivative of e^(λx) is definitely (λ^2)e^(λx) check it on Symbolab if you disagree. λ is NOT a function it is a constant. You do NOT use product rule.
(edited 4 years ago)
Reply 9
Original post by splitter2017
The 2nd derivative of e^(λx) is definitely (λ^2)e^(λx) check it on Symbolab if you disagree. λ is NOT a function it is a constant. You do NOT use product rule.


You’re right. My bad. Completely forgot that λ was a constant 😅

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