2. Using reduction of order find a general solution of x²y" + xy' - 4y = 0, y₁ = x².

Q: 5x Differentiate y= (4x – 3)* * 4x + 1 y' = (4x – 3)5 -60x – 15 y' = (4x – 3)5 - 15x + 1 (4x – 3)5 |…

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Q: y" +y' – 2y = 4e* – 2x

A: We have the given differential equation is y''+y'-2y=4e-x-2x2     …..(1) The auxiliary equation for…

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0 < x

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Q: Consider the following (x²-3x+1)y" -(x²-x-2)y'+(2x-3)y=0 on the interval I = (3,00) Verify that Y₁…

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Q: Are y₁ (1) = x, y₂(x) = ze² a fundamental set of solution for the equation r²y" − x(x + 2)y' + (x +…

A: Given thatand  are two solutions of DE

Q: Apply the method of reduction of order (not itť's formula) to find the second solution if 6y"+ y'-y…

A: Write the given differential equation 6y''+y'-y=0 in standard form by dividing by 6 throughout.…

Q: 4 y'+− y = 2; y(1) = −4 {y= X 2 = 5 -x-- 22 X 5

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Q: Find the form of yp to use in the method of undetermined coefficients y"-3y'-4y=x²e*+xe* a.…

A: Our objective is given below:

Q: Use the reduction of order method to solve the equation y" + 2y' + y = 2e-

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Q: Apply the method of reduction of order (not it's formula) to find the second solution if 6y "+ y'- y…

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Q: [v= -y +2x ,x' = 4y + x + t

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Q: 2 3 2 4. y'+=y=—y² {y x X 2 2 } 3+cx²

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Q: Find a third degree polynomial which approximates the solution to the initial va problemy" + 2xy -xy…

A: The given differential equationLets solve it using the Taylors polynomial