Find the steady periodic solution Xp (t) = C cos (ot-a) of the given equation mx'' + cx' + kx = F(t) with periodic forcing function F(t) of frequency Then graph Xp (t) together with (for comparison) F(t) mo the adjusted function F₁ (t) = x' + 6x' + 9x = 11 cos 2t Xsp (t) = (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)

Q: Q3. Solve in terms of Bessel's function, the ODE x²y" + xy' + ((lnx)² + ¹) y = 0 1²)y=0_z=lnx.

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Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

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Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

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Q: f(x) = (4x² + 3x)² h(x) = 7 (4x³ - 6x²)³ b) d) g(x)=√10x² - 5x y = 1 3/(x ³√(x + + 5)²

A: We have to find out derivative for different functions.

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Q: Find the derivative of the function. h(e)- (-1) ( 1) +]

A: Given ht=t4-15t3+16

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

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Q: Find f if f'(x) = 2 + cos(x), ƒ(0) = 10, ƒ(π/2) = 6. 2 f(x) = x² − cos(x) – (n - + - (x + 10 ) x +…

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