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Second order ODE? By sub!!!!

By using the substitution x=e2t x=e^{2t}
Find the general solution to the differential equation

4x5d2ydx2+(2x)y=x(ln⁡x)2+5,[b][/b]x>0[br] \displaystyle 4\sqrt{x^5}\frac{d^2y}{dx^2}+( 2\sqrt{x})y=\sqrt{x}( \ln{x})^2 +5,[b] [/b]x>0[br]

In all this was 17 marks believe it or not
Reply 1
Avatar for Zacken
Zacken
22
Original post by Ano123
By using the substitution x=e2t x=e^{2t}
Find the general solution to the differential equation

4x5d2ydx2+(2x)y=x(ln⁡x)2+5,[b][/b]x>0[br] \displaystyle 4\sqrt{x^5}\frac{d^2y}{dx^2}+( 2\sqrt{x})y=\sqrt{x}( \ln{x})^2 +5,[b] [/b]x>0[br]

In all this was 17 marks believe it or not


Do you need help with it or...?
Reply 2
Avatar for Ano123
Ano123
OP
15
Original post by Zacken
Do you need help with it or...?


No but I thought that some people may want to try it. It isn't difficult really but it was basically 1/4 of the paper.
Reply 3
Avatar for Ano123
Ano123
OP
15
Not sure how you would figure to use that sub unless it is a standard sub. Not sure.
Original post by Ano123
By using the substitution x=e2t x=e^{2t}
Find the general solution to the differential equation

4x5d2ydx2+(2x)y=x(ln⁡x)2+5,[b][/b]x>0[br] \displaystyle 4\sqrt{x^5}\frac{d^2y}{dx^2}+( 2\sqrt{x})y=\sqrt{x}( \ln{x})^2 +5,[b] [/b]x>0[br]

In all this was 17 marks believe it or not


Wasn't this on the AQA FP3 2015 paper?
Reply 5
Avatar for Ano123
Ano123
OP
15
Original post by TheLifelessRobot
Wasn't this on the AQA FP3 2015 paper?


yeah
Reply 6
Avatar for TeeEm
TeeEm
19
i might steal it
Reply 7
Avatar for Ano123
Ano123
OP
15
Original post by TeeEm
i might steal it


It's a nice one.

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