(a) Solve the following separable equations. (a1) y' = 2y² + ty², y(0) = 1 (a2) y' = ty (4-y), y(0) = yo > 0. 1+t (b) For equation in (a2), determine how the solution behaves ast → ∞.

Q: (c) A function y(t) is a solution of y' + ky = 0. Sup find: (i) k (ii) y(t)

A: It is differential equation problem

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A: Given differential equation is xy'' +1-xy'+6y=0 -----(1) Also,  y'' +1-xxy'+6xy=0 Here,  limx→0…

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Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

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A: y''+y'-2y=0 Auxiliary eqaution m2+m-2=0

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Q: titution: 4 11 8 }]ÿ. y(0) = [¯²]. etermined coefficients: 12 -1 · [¹² −¹5]y+[e²].

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A: y"+y=2δt-π2 ;   y0=0, y'0=4 Applying Laplace transform, we get  s2Ys-sy0-y'0+Ys=2e-π2s…

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Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: Q2) Solve: y" - 5y' +6y=H(t-1), y(0) = 0, y'(0) = 1.

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Q: Solve: x"-x+ 5 y'=t y" - 4 y-2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A: Solution:

Q: The general solution to: y'' – y' + 4y = 0 %3D is: y(x) = %3D Typle c_1 and c_2 to get c1 and c2 and…

A: We have to find the solution

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Q: (a) y" – 4y" + y' + 6y 0. (b) y" – y" + 2y' = 0.

A: General solution for the Homogeneous differential equations with constant coefficients

Q: Solve: x" -x+ 5 y'=t y" - 4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: y'+(2x-1)y-xy2=x-1; y(0)=3, explicit solution of the form y=f(x) Also: a) Determine the value of…

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Q: [Q3] Using the method of undetermined coefficients. (a) Solve y" - 2 y' - 3 y = 2e* -10 sin x, y(0)…

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Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

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A: Given; a) f(x,y)=2xy-x2-2y2+3x+4 b)y'=x3(1-y),y(0)=3 c)xy2=54.

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Q: 2) Find the general solution to 2y" - y' - 6y = 0. Find the particular solution that satisfies y(0)…

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