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junior college 2 | H2 Maths
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Hi! I am unsure of how to get the green highlighted part, pls help, thank youuuuu
Date Posted: 3 years ago
Views: 474
The 2nd line is just the simplification of the 1st. Sub in your y(0) = 0 and y'(0) = 1 and rearrange the terms.
Then, differentiate twice since its d²/ds²
If you need help with that, let me know
Then, differentiate twice since its d²/ds²
If you need help with that, let me know
Hi thank you for your help, for that part, I understand. I am unsure on how to solve the d^2/ds^2 part whereby there’s 8sY’(s) and 4Y(s)..
Product rule, basically. The s and Y(s) are two differentiable functions.
What the working doesn't show is the intermediate steps.
Give me a while , I'll type it out
What the working doesn't show is the intermediate steps.
Give me a while , I'll type it out
Okay! Thank you so much :)
d²/ds² [2s²Y(s)]
= 2 d/ds (d/ds [s² Y(s)] )
= 2 d/ds ( s² Y'(s) + 2s Y(s) )
= 2 ( s² Y"(s) + 2s Y'(s) + 2s Y'(s) + 2 Y(s) )
= 2 ( s² Y"(s) + 4s Y'(s) + 2 Y(s) )
= 2s² Y"(s) + 8s Y'(s) + 4 Y(s)
= 2 d/ds (d/ds [s² Y(s)] )
= 2 d/ds ( s² Y'(s) + 2s Y(s) )
= 2 ( s² Y"(s) + 2s Y'(s) + 2s Y'(s) + 2 Y(s) )
= 2 ( s² Y"(s) + 4s Y'(s) + 2 Y(s) )
= 2s² Y"(s) + 8s Y'(s) + 4 Y(s)
Thank you so much J!! I understand, really appreciate your help!!
Welcome
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Thank you! :)
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