4. Compute the derivatives of the following functions by using chain ru Describe your steps in detail. (a) 1 f(2) = exp 2 z = g(y) = y"S-ly %3D h(w) = V = W - I.

Q: Find y as a function of a if y(0)2, y'(0) = 3, "(0) = -13. y(x) = y″ − 4y″ − y′ + 4y = 0,

A: Given a differential equation:initial conditions are:

Q: Find y as a function of t if y(4) = 6, y (4) = 4. y = 121y" - 132y +36y = 0,

A:

Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: Find the GS of y" - y' - 12y = 0

A:

Q: Find y as a function of a if y(0) = 19, y'(0) = 26, y" (0) = 14. y(x) = y"" - 10y" + 21y' = 48e²,

A:

Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

A:

Q: Find y as a function of a if y(1) = 8, y'(1) = 6. y = x²y" + 3xy' - 35y = 0,

A:

Q: Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

A: y′′′+36y′=0y(0)=6,y′(0)=24,y′′(0)=108.The characteristic equation…

Q: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

A:

Q: Find y as a function of t if y(0) = 2, y'(0) = 5. y(t) = 100y" +9y = 0,

A:

Q: 3. Find all of the equation. (а) у —х (c) y' = x Inx (e) y" = 2xe*

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: Find y as a function of if y(0) = 19, y'(0) = 19, y"(0) = 4, y"(0) = 0. y(x) = y(4) 4y" + 4y = 0,

A: y(4)−4y′′′+4y′′=0y(0)=19,y′(0)=19,y′′(0)=4,y′′′(0)=0

Q: If f(t)= et and g(t) = 5t² - 2, use the chain rule to find the derivative of y = f(g(t)). y =…

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Q: An arrow is shot into the air and moves along the parabolic path y=x(50-x) (see figure). The…

A:

Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…

Q: Find the equation of a curve if d²y 4 = dx² (2x - 1)² the curve passes through (5, 2 ln3), and the…

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