(D²-1)y=2(1-e-2x) - ²

Q: (2v2 + 4u2v)du + (4uv + 3u³)dv = 0

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Q: (3y²-x²» = 0 ;when x = 1, y = 1 2y4

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Q: 3. d'y +16y 0 dx y(0) = 2, y (0) =-2 %3D

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Q: 2. (s-s?- t?)ds + (t + s² +t ?)dt = 0 %3D

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Q: dy dx 2₁ y x = x + 2√/ X X

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Q: Solve the differential Equation. Show complete and detailed solution.

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Q: (a). 2t²u" + 3tu'- u = 0,t> 0

A: The given differential equation is,let us substitute t=ez so z=logt and hence

Q: - = y? + xy dx

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Q: Solve u'(t) + u (t) = 5 subject to u (2) = −6.

A: given differential equation :-u'(t)+u(t) =5   subject to   u(2) = -6let   u(t)=ythen differential…

Q: d³y 1. dx³ dy + 6у — 0 dx dx²

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Q: Evaluate L {e-3(1-2) - 1¹e³¹ − 21²cos(2t) + 3e¯'sin(3t+ π) +-π)}

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Q: y = Cje² + C2xe* + C3x²e* %D O y" + 3y" + 3y' + y = 0 y" – 3y" + 3y' + y = 0 %3D + 3y" + 3y' – y = 0…

A: Given data is: y=C1ex+C2xex+C3x2ex

Q: (D² -1)y=2(1-e-2x)-1/2

A: Given differential equation is D2-1y=21-e-2x-12. To find: solution of the differential equation.

Q: 1. (у — 2)dx — (х — у — 1)dy %3D 0 |

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Q: Use truth tables to show that -(p = q) → pis a tautology. Show all intermediate steps.

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Q: (4D³ – 7D + 3)y = 0

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Q: 4 (10x3 + 15x² -7y2 - 14xy )dx tx(Sx?- 21y²) dys0

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Q: Solve the diffesential equation 2ber 十X

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