Given the following differential equation and its initial conditions y" - y' - 2y -0 with y(0) - -2 and y'(0) = 5 1. Apply Laplace Transformations to each part of the differential equation. 2. Solve your new equation for "Y(s) 3. Convert your answer back into "y(t)"

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A: For the solution follow the next step.

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A:   Solve for the derivative of the function using chain rule. 9. f(x)= esinx  

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A: We will solve the integral. 

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Q: find A-1 using Gaussian elimination and check the resul 3 -2 [1 1) A = |1 2 4. 27 1 1 Ans: A-1 = -2 ...

A: Explanation of the answer is as follows

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Q: draw a tree diagra w : fLx, y,z,N n and write chain rule! ニ y = f lu,v) , Z=f lu,V), N= f (u,V).

A: Here we will draw tree diagram and write chain rule,

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A: dydx=-xyRearrange the equation;y dy=- x dxf(y) dy = f(x) dxYes,the given equation is variable separa...

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A:

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A: 3xy ^ 2dx + (3x ^ 2y + 4y ^ 2) dy = 0  

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Q: 4. DETAILS LARAPCALC10 3.2.004.EP. Consider the following. f(x) = -4x + 3x + 2 Find f'(x). f'(x) -8x...

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A: I have stated the used formulas in the solution

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A: As per guidelines we can answer only one question at a time, so if you need more answers kindly repo...

Q: satisfying

A: We will obtain the particular solution. 

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A: Given a vector u that makes an angle θ with the positive direction of the x-axis .Then , u = u cosθ ...

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A: Slope of the Normal Line to the graph of f(x) is  -1f'(x). Equation of the line : y-y1=mx-x1 where, ...

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A: Given problem:-

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Q: 2. For the following complex numbers; peform the indicated operations. Expressresultsin rectangular ...

A: Given:  za=-2-5izb=2.15e4.18izc=1.75cos165°+isin165°zd=0.745∠-36°ze=1+3izf=0.953cos324°+isin324°zg=2...

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A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

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A: Solution :∫cos6xcos3xdxNote :2cosacosb=cosa+b+cosa-b12∫2cos6xcos3xdx12∫cos6x+3x+cos6x-3xdx12∫cos9x+c...

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A: To Convert Rectangular coordinates (x,y,z) to Cylindrical coordinates (r,θ,z) :           As x= rcos...

Q: 4 -5-4 -3 -2 -3 2.

A: From graph  as x approaches to - 2 from the left side f(x) approaches to +∞