Find the solution of the given initial value problem. ty' + 3y = t² − t +5, y(1) = 6, t > 0 y =

Q: y', In(y) 1 y(e) = 1. x² In(x)

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Q: Solve the initial value problem: 0 2 y = [ -2 -1 ]y, yo = [²] y' y(0) -2 2

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Q: Find the general solution to y''-1=0

A: y''-1 =0y'' = 1y' = ∫1 dxy' = x + By =∫(x + B) dxy = x22 + Bx + A

Q: particular solution

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Q: The unique solution to the initial value problem is y(t) = 9e−²t + 4t + 7. Determine the constant y…

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Q: Find the general solution y''-y'-2y=0

A: Given the differential equation y''-y'-2y=0. We need to find the general solution of the above…

Q: The equation y² = Cx is the general solution of 2x A. y' = 2 y 2y B. y' = 22/ C. y' = D. y' = 2x

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Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: 6. Solve the initial value problem: (2² + 2y^) Jy dx = xy, y(-1) = 1

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Q: Solve the following difference equation with initial conditions: 12Yn + Yn+1 = Yn+2, Y₁ = −2, Y₂ =…

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Q: dy Q.2 Solve x/1+ y² + yv1 +x² = 0. dx

A: The expression is x1+y2+y1+x2dydx=0 Multiply both sides by 11+x2·1+y2…

Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: Find the solution of the difference equation Yn+24yn+1+3yn = 2.3" with initial conditions yo = 2, y₁…

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Q: What is the general solution to y''+y=0. Show the solution.

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Q: Find a special solution of yn+2 - Yn= fo = constant by variation of parameters.

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0