3. d² y dx-² 5 -3x4 y d³y dx-3 = x ln x

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A: Here we have

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A: Topic =Differential Equations

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A: The sum of Infinite Geometric Progression of the form ∑n=0∞an where -1<a<1 is given by 11-a

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Q: 3 ³√x - 1 lim X→1 X-1

A: limx→ 1x3-1x-1By L'Hopital rules,=limx→ 113x231Plug in the value x=1=13· 1231=13

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A: I have done it step by step. The simplification is wrong.

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A: Note: Since the student has asked to solve parts (d), (e), and (f). So we are solving accordingly…

Q: 1. S e²x dx √25-4e4x

A: I=∫e2xdx25-4e4x This can be written as: I=∫e2xdx51-425e4x I=∫e2xdx51-25e2x2

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A: A detailed solution is given below

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