Given y₁ (t) = t² and y2(t) = t¹ satisfy the corresponding homogeneous equation of t²y" - 2y = 2-t, t > 0, the general solution to the nonhomogeneous equation can be written as y(t) = yp(t) + C₁y₁(t) + c2y2(t). Use variation of parameters to find y, (t). Yp(t) Preview

Q: Find a second linearly independent solution and write down the general solution: x²y" - 5xy' +9y =…

A: To find a second linear independent solution of the given problem where one solution is given.…

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

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A: We have to solve for a linear equationPty''+Q(t)y'+R(t)y=S(t)

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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.

Q: Eliminate the constant: 3r y=c₁₂e²²+c₁₂e² Oy"+y'-6y=0 Oy"+ 5y¹+6y=0 Oy"-5y¹+6y=0 Oy"-y'-6y=0

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Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

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Q: kpression for "12 times x."

A: Times means multiplication. Sometimes it is denoted by dot.

Q: а. у' +3у%38, у(0) %3D4 b. 1 xdx+dy= 0, y(0)=8 y c. senxdx+ ydy=0 y(0)= -2 d. y' +2xy2 = 0, y(0) = 3

A: y = -srqt(2+2cosx) is a solution of:

Q: Let y be the solution of y'+y=x, xER,y(-1)=0. Then, y(1) 류를 ²-28² 2-2e -

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Q: У). y), where

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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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A: The Solution is given below

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A: with initial positions and initial velocity