Consider the following initial value problem: y" + 6y' + 8y = 8(t — 5) + u₁0(t); y(0) = 0, y'(0) a) Find the solution y(t). y(t) = where c= + + and d = || = 2 uc(t) ua(t)

Q: - 2. (4)y=x'. D² +5D+

A: Given differential equation is, D2+5D+4y=x2.

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: 4. (D² +D-1)² y =0 ,when x= y = 0, y' = y" =1, y" = -1

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Q: P(t)y'' + Q(t)y' + R(t)y = S(t) is this a linear equation?

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Q: y" + 2y' + y = e* lnx (where x > 0)

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Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: y" (t) + 2y' + y(t) = 8t²e-t.

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Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' + y = 0. If W (y1, Y2)(2) = e² , then…

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Q: dx 2. Find the value of at y=1 if x=z³+4z and z= (y² + 2y)²/³. dy

A: We have to use chain rule while differentiating.

Q: 25. Let y = y₁ (t) be a solution of y' + p(t)y = 0, and let y = y₂ (t) be a solution of y' + p(t)y =…

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Q: 3. Is y(x) = C,sin2x + C2cos2x, where C1 and C2are arbitrary constants, a solution of y" + 4y = 0?

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Q: Find the solution: y" + 3y' + 2y = 12x2; y(0) = a, y'(0) = b

A: We have to find the solution to the given equation.

Q: Eliminate the constant: 3r y=c₁₂e²²+c₁₂e² Oy"+y'-6y=0 Oy"+ 5y¹+6y=0 Oy"-5y¹+6y=0 Oy"-y'-6y=0

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Q: 1. (x2 + y² + 1)dx + x(x-2y)dy = 0 (Non-exact Equation) Ans: x² - y² + xy - 1 = cx

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Q: (t+ 9) y" + 2t y = 0 y(3) = 2n У 13) 2/3

A: We solve the given IVP  (t2+9)y"+2ty'=0.....(1) y(3)=2π,y'(3)=2/3

Q: (C) y" + 21y+8x=y" + 5y' + e²*

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Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

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Q: Use variation of parameters to find the particular solution to y'' + 5y' + 4y = 2e-34 Y(t) = […

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Q: 2. 2xydx+(4y+3x²)dy = 0; y(1)=1 {y²+x²y³ =2}

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Q: If r(y) = e³y² +3 find r'(y) =

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Q: Solve the following initial value problem: y" + 8y + 65y = 8(t – 8); y(0) = 1, y (0) = 3. functions,…

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Q: (Dー)y=0 findyc

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Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

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Q: (a) y" – 4y" + y' + 6y 0. (b) y" – y" + 2y' = 0.

A: General solution for the Homogeneous differential equations with constant coefficients

Q: (D3+25D)y=32cos24x and y(0)=y'(0)=y''(0)=0   find y(x)  regards

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Q: e + xy + 4x = 1 ise y"(0) =?

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Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

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Q: Consider the following equation: x?y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 1. Verify that y, (x) = x…

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Q: What is the particular solution if y(1)=0? 1/2 xy = y + (x² + y³)"

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Q: 4- (x2 + y2 + x)dx + xydy = 0

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Q: b) x²y + xy = 1 x>0 y(1) = 2

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