The solution for y″+2y'+y=2e¯³ is? a) y = C₁¯* + С₂xe¯* +x²e¯* b) y = C₁e¹ + С₂x¹ + x²e¯† -x c) y = C₁e¯³ + С₂e³+x²e²¯x d) y = C₁e + С₂xе¯³ + xe¯¨*

Q: (a) For each of the functions below, determine whether it solves equation A), (y')² = 1 – y². i)…

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Q: Ixe A) e¯(1 − x) + C el-r 1-x B) -I dx = +C x C) -e (x + 1) + C D) −æe¯ª + C E) e(x + 1) + C

A: Topic = Integration

Q: 2) vting daplace toansfóöre, Solve x" Zt)+4x'Lt)+3=(4) uing = 10 gint yeren that xco) = -3t Ans: ILt…

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Q: Find the general solution of y " - 7y " + 16y' – 12y =0 given that r = 3 is a root of the…

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Q: 2) / x² - y²) dx + (x² - ²xy) dy = 0 6 ,2 1 21 COCX

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Q: y" +2y = 2x+5-e-2r y""-6y"=3-cosa

A: These questions are about ordinary differential equation.

Q: Solve y"-6y' + 5y = 0 A) y = c,e* +c,eS* B) y = c,e* + ce C) y = c,xe* + c,e D) y = c,xe* +c,xe

A: To solve  y"-6y'+5y=0

Q: For cos2(xy) =-, evaluate y' when x = 1. 4

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Q: Q1: Solve the following ODE a) y" + 2y' - 6y = 0 b) y'"- 6y" +12y' - 8y = 0 c) y"+y'- 2y = x².

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Q4) A-Determine the particular solution of the equation y"-y=0 for yo-=0, yo'= -2

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Q: Find the solution of the given ODE a. 1 - 2 = Cx b. 1 + (-)² = Cx c. 1 - * = Cx y d. 1 + (-)² = Cx…

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Q: 9) Solve: (x + y)dy-(z-y)dx=0 a) x² + y² = C b) z² + 2xy + y² = C c) z²-2ry+y²=C d) z²-2ry-y²=C

A: We need to solve D.E.

Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: If u = x² tan equal to (a) (c) x - y x + y - 2 + V² 2 X X -, y x + y x - y x² + y² 2 X - y - y² tan…

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Q: y" = 5sin (2z) denkleminin çözümü aşağıdakilerden hangisidir? %3D

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Q: y' + E) y = xy? 2

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Q: Solve for x + y (EZ) if i) x² - y² = 24, ii) xy = 35

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Q: Solve the equation 4 x² y" + 4 x y' – y = 0

A: The given opinions and incorrect. There can't be x in power. In particularly x(-x/2) can't be…

Q: What is the auxiliary equation for y"+by'+c=0, b & c is constant. What are the condition for this DE…

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Q: Solve y" - 6y' + Sy = 0 A) y = Ge +6;e B) y = ce" +ce*" y = q,xe* +6,e“ D y = G,xe" + e,xe

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Q: 3) y`+y=xe*

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Q: 4. Classify and reduce the following equations to a canonical form: (a) yu -x*u, = 0, x>0, y>0. (b)…

A: To classify and reduced in canonical form of the given equation is..

Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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Q: 7) Solve the first order equation. c ER dy 4 dr x = x*e* a) y = x°e* – x³e* + cx5 c) y = x5e* – x+e*…

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Q: 1 y" + 3y' - 18y = 0 2 y"-14y' +49y = 0 y" + 2y' +10y = 0 y"" — 7y — бу = 0 3

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Q: = (e+ tan())“ then what is the value of y' (0)? a) 0 b) -1 c) 1 d) -2 e) 2 191 a) a b) c) C d) d.

A: To find the derivative of y

Q: In what form should the particular solu tion be sought for the equation y(1) + 2y" + y" + 2y' =…

A: Consider the equation y4+2y'''+y''+2y'=xe-2xThe characteristics equation of the homogenous equation…

Q: If f(x) = cos (-x) + 3x + 2, xE [0,1], then f"(5) = %3D A) cos + 17. B) cos()+17" (Sm C) 0. D) 2. E)…

A: Solution of question as follows

Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…

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Q: Solve the following 1 1) y dx + x² + y? dy = 0 x +y 2) (3x? In x+ x² –y) dx- xdy = 0, y(1) = 5 dy…

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Q: 1 b)y" + y = ; 1+sinx

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Q: 35) y = -4 sin x 4+ 2+ 2n -2+ -4-

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Q: In what form should the particular solu tion be sought for the equation y(4) + 2y"' + y'" + 2y' =…

A: We will solve it by undetermined coefficient method Let the particular integral with respect to x is…

Q: Q1) solve all these first order diff questions with appropriate method of solutions dy _ y²+xy?…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…