9. Solve the initial-boundary value problem: Utt 4uxx = 0, u(0, t) = 0, u(1, t) = 0, u(x,0) = 0, ut(x, 0) = x, Remark: Solution of the eigenvalue problem X" + XX = 0, X(0) = 0, is An = n²r², Xn(x) = sin(nπx) for n = 1,2,.... x € (0, 1), te R, tER, x = (0, 1). x = (0, 1), X(1) = 0.

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Q: 4x-y<-1

A: Given  4x-y&lt;1 Can be rewritten as y&gt;4x-1 So we take the area above the line y = 4x -1 And all…

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A: This question is from linear partial differential equation.

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Q: This is the solution of the Cauchy - Euler equation xy" + 5xy' + 20y = 0 %3D O y = C1x4 cos(4 ln(x))…

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Q: 6, Solve the IVP 3w" -u'+ 2u0. u(0) = 2, u'(0)-0

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Q: 13. y' + ty = ry* Answer": y' = 3/(3rr + 2 + Ce(3/2)t²)

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Q: 6. (E) Prove that there are no solutions to the equation 2x² + 5y² = 32² in positive integers (x, y,…

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Q: Solve the initial value problems: (a) / = 6+ 5y + y?; y(0) = 0 (b) / + 2.ry + ryt = 0; y(0) = 1

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Q: х?у' + 2ху %3D In(х), у(1) 3D 2

A: To find: The solution of differential equation x2y'+2xy=lnx, y1=2. Concept used: The solution of…

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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

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Q: Solve the non-homogeneous Cauchy-Euler equation x²y"-2xy' +2y=6x² +4 lnx, x>0.

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Q: Solve the IVP 22 + 1ox+1 %3D y Co) =0, y'(0) = -6 Osi ng the quasi-polynomial method.

A: y''-3y'-4y=0 D2-3D-4=0 D2 -4D+D-4=0 (D+1)(D-4)=0 D=-1,4 Complementary function =c1e-x +c2e4x

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A: To solve the following Cauchy problem.

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Q: 1) Eliminate the constants from the following equations: y = x² + C₁e²x + С₂e³x y' = 2x + 2C₁e²x…

A: NOTE: As per our guidelines, I have solved the first problem. If you want solutions of rest, kindly…

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Q: Define fct) = {est + e + cast if t 1/2 t>"/2 solve y(3) - 2 y(2) + ý' - 2y = f(t) y (0) = 1, y'(0) =…

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Q: 3. Determine whether the method of separation of variables can be used to replace uxx+2uxt+ut = 0 by…

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