1. Find the value of (0) for a solution (x) to the initial value problem: 6y" + y' — 2y = 0; y(1) = 2, y’(1) = 7². (a) e ² + e (b) e²-e 2 (c) ez-e (d) e²² +e²²³ (e) ez - e²² 2|3 3

Q: Solve the following D-E 1) xy" – y2 – 2y' = 0

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

Q: Consider the equation y"-y-2y = 0. Assume that y₁ (1) = ¹ and y₂(1) = e² form a fundamental set of…

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Q: Solve the following initial value problem: (2x + 4y)dx + (y – x)dy = 0, y(1) = 0.

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Q: 13. Find an equation of the curve that passes through the point (1, 1) and whose slope at any point…

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Q: 6. Determine the values of C₁ = 922 @ +923 and C₂ = 924 @ +925 if y(t) = e2¹ (C₁cos(1) + C₂sin(t))+…

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Q: 2. Use the undetermined coefficients method to solve: y"-6y+9y=2e3+ 31²; y(0) = 0, y'(0) = 1

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Q: Suppose the equation y"+p(t)y'+q(t)y = f(t) is non-homogenous, has a particular solution y(t) et2,…

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Q: 5. (x² + y² + x) dx − (2x² + 2y² −y)dy = 0 [Answer : x - 2y + log(x² + y²) = c]

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Q: b. Solve the initial value problem: f (x)= sin x +e2, f(0) = 4 1 f (0) 2

A: Given: f''(x) = sin x + e2x, f(0) = 14 and f'(0) =12

Q: Solve the following IVP: X' = AX + f(t), where 2 -1 A = 3 -2 and X(0) = ( : -3 2 f(t) 10t ||

A: First we need to find the eigenvalues and eigenvectors of a then find the complementary solution of…

Q: If y1=x is a particular solution for the equation x2y''+xy'+q(x)y=0 ; (x>0); then q(x)=? Using the…

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Q: Solve the following D.E 1) xy" – y2 – 2y' = 0 2) y³y" – 3y*y' = 0 3) yy" – 3y = 0 4) y?y" – 2y' = 0…

A: AnswerGiven differential equationxy"-y'2-2y'=0 --(I)Let w(x)=y'(x) which gives w'(x)=y"(x)

Q: (D³ - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. A y = (-1+ 2x)e²"+2e=x B y = (-1+ 2x)e-2r+e2r C y…

A: Given differential equation is (D3-3D-2)y = 0 with x=0,y=0,y'=9,y''=0.

Q: (C) y" + 21y+8x=y" + 5y' + e²*

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Q: Solve the equation (x + 2y-4)dx - (2x + y - 5)dy = 0. (x + y - 1)² = c(x-y-3) (x-y-1)² = c(x + y -…

A: x+2y-4dx-2x+y-5dy=0

Q: 2x- (ii) Given aty=b²x-y and a 4x+3 = bx-5y, show that 3y-6x=7x² +5y²

A: (ii) Given ax+y=b2x-y and a4x+3=bx-5y We will use logarithm properties to solve the given:

Q: (D) e(-1-v2)x + cze(-1+v2)x If r2+2r-1 = 0 is the characteristic equation of a homogeneous D.E. with…

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Q: (9x2+y−1)−(4y−x)y′=0,y(1)=0

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Q: (c) Solve the following IVP by separating variable. 2(y - a)da + (3a + 4r + b)dy = 0 Using initial…

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Q: Q(2): Find the general solution of x³y" – 3x²y" + 6ry' – by = xª In x. %3D

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Q: Ify = e is a solution to y" - By' + ky = 0, what is the value of k? (b) 6 (c) 6 (d) none of these…

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Q: (b) Solve the following initial value problems: (2xy-9x²)+(x² + 2) t+2y-2 +3 sint; (1) = 0; y(0) = 3…

A: Solution of the initial value problems

Q: "+2y(y)² = 0 =1^²)={1^²/ LV=X+C₂ y(x) = c₂e¹1* - 1 . (C₂-y)² + x² = C₁ :C. -In(c 2) 71

A: Given differential equation

Q: Q(4) Find the general solution of dy =(r- y+ 5). dr

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Q: (c)2a) (c)(n)(z)(z) = e/(a) (c)(K)(z)) ¹/2 (b)(y) (6)(x) (y) Solve for K [(g) (m) (f)(K)

A: We have to solve for k.

Q: Q4. (a) Show that the substitution r= e' reduces the equation ar'y" + bry' + cy = g(x) to an…

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Q: 4. Use th shooting method to solve 2+ 1 y(0)- 1. y(2) = 1.

A: Given: The given equation is y''=y22+xy(0)=1y(2)=1

Q: In which form should we look for the particular solution of

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Q: 5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*

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Q: j(x) = (2)(x – 7)3/2 + 1 EVALUATE                                              SOLVE j(11) =

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Q: Suppose xe¹ - 4y = 3x + 1 + le¯¹ and y(1) = -1. Find: y (1) =

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Q: y(7) + 5y(6) + 13y(5) + 17y(4) −13y'''−33y'' −65y' + 75y = 0 What is the general solution of the…

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Q: 4. Aşağıdaki denklemi y(2)=1 başlangıç koşulu için çözünüz dy (x² + 1 ) + 4xy = x dx

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Q: (a) y(x) = x+2√x+5; (b) y(x) = e³ cos(4x); (y − x)y' = y − x + 2. y" - 6y' + 25y = 0

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Q: Solve initial value problem f(x) = 3/T+ 2x:f(0) = 2 .

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