Given y1 (t) = t and y2(t) = t satisfy the corresponding homogeneous equation of t'y" – 2y = t4 + 2, t > 0 Then the general solution to the non-homogeneous equation can be written as y(t) = c1y1 (t) + c2Y2(t) + Y(t). Use variation of parameters to findY (t). Y(t) =

Q: Eliminate the constant: 2x 3x =c₂₁e²x + c₁₂e³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

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A: Given: f(x) = x2 +1x − 2; a = 3

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Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Find the the stationary points and the local extreme values of the function f(x, y) = −2x/x2 + y2+1

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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: homogeneous equation

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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: 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: If y = v3x , then y' is A. -1/2 B. V3 x -1/2 С. /3x V3 D. 2 V3 -1/2

A: Given y=3x

Q: Let y be the solution of y'+y=x, xER,y(-1)=0. Then, y(1) 류를 ²-28² 2-2e -

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Q: Two classmates Sali and Arun simplified two different expressions during the revision hour and…

A: Just rationalize it.

Q: У). y), where

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Q: Eliminate the arbitrary constant. 2x y=c₁' e B A y"-y'- 2x=0 C -X (D) +c_e 2 y"-y'-2y=0 2y"-y'-2x =…

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Q: se Newton-Raphson Method to find the approximate solution of the nonlinear equation f(x) giv en as…

A: To approximate the solution of the below equation using the Newton-Raphson Method. x3−x−1=0

Q: Show that a linear equation dy a(x)- + b(x)y = c(x) d.x %3D is exact if a' (x) = b(x).

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Q: Find general solution of U" + U = 0.

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Q: 9. (1) Find a second solution of the given equation. t²y" +2ty' - 2y = 0, t > 0, y₁(t) = t. (2) Find…

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Q: Solve for the solution for the equation: y' + xy = 6x/y with the condition of y(3) = 6.

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Q: Solve the DE: (2-x) y³ +(2x-3) y'' - xy' + y = 0, x<2, given that y(x) = ex is a solution of the…

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Q: Let u (41, U2, Uz). Explain why u•u > 0. When is u•u 0?

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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: Is the equation y '(t) = 2y - t separable?

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Q: [v= -y +2x ,x' = 4y + x + t

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Q: y=cJ,(/2x) +c,J,(/2x)is solution for x?y "+xy'+ (2x² – 4) y=0

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Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

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Q: If y = f(x) is the solution of y" – 9y" +26y' – 24y = 0, f(0) = 4, f'(0) = 15, f" (0) = 44, then

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Q: Eliminate the Arbitrary Constant: y = c,x² + c2e¬* а. 2(х + 1)у' — (x? — 2)у" — х(х + 2)у %3D0 b.…

A: topic - differential equations

Q: solve for the homogeneous coefficient   (x²+2yx-4y²)dx-(x²-8xy-4y²)dy=0

A: Consider (x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0⇒ (x2+2xy-4y2)dx=(x2-8xy-4y2)dy⇒dydx=x2+2xy-4y2x2-8xy-4y2To…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.