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Calculus/succesive differenciation

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Expert: Alon Mandes - 2/22/2010


Question
y=e^ax sin bx prove that y2-2ay1+(a^2+b^2)y=0

Answer
y=[e^(ax)][sin(bx)]
Let's differentate :
y'=[e^(ax)]'[sin(bx)]+[e^(ax)][sin(bx)]'
y'=a[e^(ax)][sin(bx)]+[e^(ax)]b[cos(bx)]
Let's differentate 2nd time :
y''={ a[e^(ax)][sin(bx)]+[e^(ax)]b[cos(bx)] } '
y''={ a[e^(ax)][sin(bx)]}' + { [e^(ax)]b[cos(bx)] }'
y''= (a^2)[e^(ax)][sin(bx)]+a[e^(ax)]b[cos(bx)] +  a[e^(ax)]b[cos(bx)]-[e^(ax)](b^2)[sin(bx)].

I will leave it to you from here to show that the last expression is actually :
y''=2ay'-(a^2+b^2)y .

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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