10) Solve the linear nonhomogeneous equation for the general solution. 2e* y" – y =- ex + e-x Hint: S dx = tan¬1 x 1+x2 a) y = c,e* + c2e¬* + e* tan¬1e* – 1 + e-* tan-1 ex b) y = c,e* + c2e¬x – e* tan-1 e* + e¬* tan¬1 e* | c) y = cqe* + c2e¯* d) y = c1e* + Cze¬* + e* – 1 + e¬* tan¬1 e*

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A: Given differential equation is (D5-2D3-2D2-3D-2)y = 0

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A: I have used the rule for composition of function and multiplication of functions

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A: To solve the given differenrial equation.

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Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

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Q: (D² - 9)y = 0. (A) y = e*(c,cos2r +c sin2x) B y = c,cosh 3x + c,sinh 3x y = c,cosh – 3x + c,sinh 3x…

A: Solution

Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

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A: We will solve the problem

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Q: Solve

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Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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