the ihitlal value problem (0) = %3D %3! a. Form the complementary solution to the homogeneous equation. ýc(t) = c1 + C2 b. Construct a particular solution by assuming the form p(t) = ãeª + bt +č and solving for the une

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A: The detailed solution is as follows below:

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A: See the detailed solution below.

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Q: Find the solution of the initial condition problem: j + t°ÿ+ 3t?y = 0, , y(0) = 1, ý(0) = -1. |

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

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A: According to our guidelines we can do only one question it multiple question is posted. Please post…

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A: Given x2y" + 2xy' - 2y = x2 ,   y1 = x-2,  y2 = x

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A: Given                      ∂u∂t=2∂2u∂x2,     0<x<1, t>0,                  (1)…

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A: Note:- As per our guidelines, we can answer the first part of this problem as both the parts have…

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A: Given :y'''+y'=0

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Q: 1. Solve the following homogeneous equation, using direct factorization: y"' + y' = 0

A: The given data is: y'''+y'=0 To solve the given homogeneous equation.

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A: Explanation of the answer is as follows

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A: The given differential equation is solving through the variation of parameters below.

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A: solution of non differential equation

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A: According to question given thatyp=v1t+t2v2(t) is a aprticular solution  of ty"-y'=4t

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