.. Solve y'" + y' - 2 y = 0, y(0) = 3, y'(0) = 2 %3D yt) =

Q: y = 3/4 x 4/3 = 3 x 1/3 + 5, 1 <x<8 (Ans = of unit)

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Q: Differentiate. ax + b f(x) %3D Cx + d f '(x) =

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Q: Find y' for y=3x-3-7x-¹. y'=0

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Q: Find y' and y". y = e4e* y' = y" =

A: The given equation is y=e4ex. Calculate the value of y' and y''.

Q: Find y' and y". In(2x) y = 1- In(32) y' y"

A: The given function y = ln(2x)/(x^5):   Find the first derivative of the function y = ln(2x)/(x^5)…

Q: Find y'. In(5x) y = 4x y' =

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Q: Calculate y'. y = ln(x ln x)

A: Given: y=lnxlnx The objective is to calculate its derivative. Chain Rule for Differentiation: ddxf…

Q: 2) y' – (cotx)y = -(2cosx)y2 %3D

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Q: Find y'  if e x/y      = x   -y

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Q: Calculate y'  if y=1/(x+(x)^1/2))^1/3

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Q: V(x) = (5x³ + 3)(x* – 2x) V'(x)

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Q: Answer y = ce-((lnx)^2)/2

A: Given differential equation is,

Q: y" - y' = -4 y(x) = %3D

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Q: Find y' and y". In(3x) y = y" %3!

A: Given y=ln3xx6

Q: Find f. f"(x) = -2 + 18x – 12x2, f(0) = 3, f'(0) = 14 f(x) = %D

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Q: r(x) = 3x/4- x0.1/3 + 5/4x1.1 - 3 r'(x) =

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Q: y-5y't 4y =O x10)-5 y'l0)=2

A: We have to find the particular solution of the initial value problem…

Q: Solve y' = 4xy - 2x, y(0) = 20 y(x) =

A: Given: y'=4xy-2x and with the initial condition y0=20 To find the general solution of the given…

Q: Find y'. y = x − ln(3x) y' =

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Q: Solve y'= 10xy - 2x, y(0) = 5 y(x) =

A: To solve the following initial value problem. y'=10xy-2x, y0=5

Q: Find g'(x) if g(x) %3D Зx е бх

A: Product rule of the derivative is, (uv)’=u’v+uv’ where u and v are the functions of x.

Q: Find y' and y". y = x² In(9x) y' = x + 2x ln (9x) y" = 3+2 ln( 9x)

A: Given function is Differentiating with respect to x by using product rule of differentiation, we…

Q: y' = = x/n(x)

A: We can find the derivative of the given function by using logarithmic differentiation.

Q: - 1 Find y' for y=7x7 + 9x¯ y' =

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.