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: 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: Determine all solutions. y'= (x-y + 3)²

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Q: Find the solution to the equation y' - y = x2y2

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Q: y' = 3x²+y² xy ; given that y(1) = 1 ; solve for y when x = 2

A: The given equation is; y'=(3x2+y2)/xy, y(1)=1.

Q: + ¹² = 4t, where y'(1) = 1 and y(1)=2. 4) Solve y" +

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Q: Put the equation into the form x'(t) = g(t)h(x), and solve by the method of separation of variables.…

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Q: y' = (1 − x²)²; y(15) = 149,645

A: differential equation

Q: .1 Solve the equation x'y"-3xy'+3y 2x'e by method of variation of parameters.

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Q: Find g'(4) given that ƒ(4) = 7, ƒ'(4) = −1, and g(x) = √xƒ(x). Answer:

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Q: 3x e The y, of y"-6y'+9y = x2 by using variation of parameters is: .A Y,(x) =0 .B 3X Y,(x)= -In(x).…

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Q: Solve :     x²y"-2x(1+x)y'+2(1+x)y = x3

A: Given: The second order differential equation is x2y''-2xx+1y'+2x+1y=0