Given yi (t) t² and y₂(t) = t¹ satisfy the corresponding homogeneous equation of t'y" - 2y = -2t¹-3, t> 0, the general solution to the nonhomogeneous equation can be written as y(t) = y(t) + C₁y₁(t) + C2y2(t). Use variation of parameters to find y, (t). Yp(t) Preview

Q: Solve y''+2y'+2y=δ(t−1) +U(t−2), y(0) = 2, y′(0) = 1.

A: Given The given differential equation is y"+2y'+2y=δt-1+Ut-2. y0=2, y'0=1. Apply formula Laplace…

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Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

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Q: Solve y + y = 2y = 0, where y (0) - = 3 and y (0 y(t) =

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

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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A: Given differential equation is t2y''+5y'+(t+2)y=0   Also, given y1, y2 are Linearly Independent…

Q: Solve for a linear equation? P(t)y'' + Q(t)y' + R(t)y = S(t)

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Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

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Q: Find the linearly independent solution of the equation y"+xy'+y=0 around the point x=1.

A: We will find out the required solution.

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Q: Eliminate the arbitrary constant. 2x y=c₁' e B A y"-y'- 2x=0 C -X (D) +c_e 2 y"-y'-2y=0 2y"-y'-2x =…

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Q: Determine 4sin(x); the value of the arbitrary constants y(x) = C₁e* + c₂e¯* + y(0) = 1, y'(0) = -1…

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Q: Consider the following equation: x?y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 1. Verify that y, (x) = x…

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Q: What is the equilibrium solution of the equation y '(t) = 2y - 4? Is itstable or unstable?

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Q: (2y² + 3x) dx + 2xydy = 0 Determine an appropriate integrating factor (x) or (y) that transforms the…

A: Solution :