Find the solution to Integro-Differential Equation.

Q: cosy dx + (1 + e¯*)siny dy = 0

A: By separating the variables on each side  we can integrate them easily. Given, cosy dx+(1+e-x)siny…

Q: x = c, e" + cz e- 21 e" O x"- 2x'- 3x 8 e O x" + 2r'+ 3x = 8 e' O x" - 3x'- 2r 8 e O x"- 2x'+ 3x = 8…

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy - y = 0 dx + x + 4y dt — 10%; х - | dt

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Q: xdy − ydx + x³dx = 0

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Q: Form the differential equation for the function x+2y=a sin3x-bcos3x

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Q: Solve the differential equation using Separable of variables.

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Q: 3y"-Gy'+6y by = = e sec x

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Q: dy 2xy dx 1+x² =

A: Sol:- dydx=2xy1+x2A first order separable ODE has the form of Ny·y'=MxSubstitute dydx with y' y'…

Q: 4. y"-2y'+y =7+ 75 sin 2.x

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Q: d²y dx² 3 7 + 3y (dy) 2 + y ² (dy) ² 3 0 = 5x

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Q: Transform the equation y' differential equation. O (1 + x²) dx - dy = 0 O (1 + x²) dx 2x 0₁dx 1 + x²…

A: y'=2xy1+x2

Q: (r+sin 0- cos 0) dr + r (sin 0 + cos 0) d0 = 0

A: (r+sinθ-cosθ)dr+r(sinθ+cosθ)dθ=0 lets rearrange and then integrate

Q: w (1) = 1 -+ xtu (t) dt, u (0) = 0

A: The given integro-differential  equation is                u'(x)=1-13x +∫01xtu(t)dt with initial…

Q: dy 4x+xy² dx y-x²y =

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Q: 3. მ მე2 + (x + ყ) მ2 მყ2 = 0 =

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