Find the solution of the given initial value problem using Method of Variation Parameters: y'' + y = sec x; y(0)= 5, y'(0)= -3

Q: max value for y

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Q: Solve 2y'' - 5y' - 25y = 0, y(0) = 0, y’(0) = = y(t) = - 37.5

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Q: Solve. y'' – 36y = et The general solution will be 6t 6t y(t) : cje + c2e +

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Q: Given f(x) = In(- 4e" – 13), f'(x) = %3D

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Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: please use the method of variation of parameters to determine the particular solution y'"+30y"…

A: The given differential equation is:y'''+30y''-4000y=e-20x

Q: First, solve the following IVP, y' = (15x + yr1 . 15 , y(0)=1. Then calculate y(12).

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Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

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Q: If h(x) = V5 + 4f(x), where f(1) = 5 and f'(1) = 2, find h'(1). h'(1) =

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Q: Solve for y(x):  y’’ – 5y’ + 12y = 0; y(2) = 0; y’(2) = -4

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Q: Solve y'' + y' — 6y = 0, y(0) = 8, y'(0) y(t) = = - 9

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Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: Find y' if y = In(9x² + 5y²). y' = X

A: The given data is: y=ln(9x2+5y2)  Find y'

Q: solve by bernoulli y' + (8/x)y = x6y4

A: We will find out the required general solution for given Bernoulli's equation.

Q: 3. Given the following graph and A(x)= [f(t) dt, find: A(4)= 4 y=f(t) 3 A(6) = 1- A(10)= A'(x)= -2

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Q: y' = (1 − x²)²; y(15) = 149,645

A: differential equation

Q: y''+4y=0  y(0)=5 , y'(0)=6 find the start and end values Y(s)=?

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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: 8) y'+y=17 sin(2t), y(0) =-1.

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Q: Find g' (6) given that f(6) = - 3 and f' (6) = 6. Enter the exact answers. (a) g(x) = 7x² – 6f (x)…

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Q: Solve the following 2nd order D.E using variation of parameters method: y'' + 2 y' + y = e^(-x)

A: The non homogeneous differential equation is given as y''+2y'+y=e-x Corresponding homogeneous…

Q: Find the value of a for which the equation y''+a^2y=0 has non trivial solution such that y(0)=y(pi)…

A: Since we have that                  y''+a2y=0                y(0)=y(π)   and y'(0)=y'(π) Then…

Q: Find f. 4 f'(x) = 1- Ex) = %3D

A: This is a problem related to integral. Based on the given differential equation we will calculate…

Q: Solve the equation y' = x/r? + 1/(ye") and graph sev- eral members of the family of solutions (if…

A: the given differential equation is: y'=xx2+1yey we have to graph the several members of the family…