Eliminate the arbitrary constant from the given equation: y=c1e2x cos3x +c2e2Xsin3x A y"=10y'-13y=0 B y"-4y'+13y=0 (c) y"+4y'-6y=0 D None of these E) -2y"+ 4y'+13у-0

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A: First find out the centre of given conic then write the equation of family of lines passing through…

Q: 8. Solve the ff DE y" -9y = 0 y = c₁e³x + c₂e-3x y = c₁ cos 3x + c₂ sin 3x y = ³x (c₁ cos 3x + c₂…

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Q: 2. Find a homogeneous linear equation with real, constant coefficients that is satisfied by: y = 6 +…

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Q: Write only the corresponding differential operator of y''+8y'-8y=0

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Q: 1. cosysin2xdx + (cos²y – cos²x)dy = 0; by treating x as the dependent variable

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Q: A particular solution of x²y" + xy' + (x? – 0.25)y = 3x3/2sinx, x>0, y,(x)=x-1/2sinx, y2(x)=x1/2…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 1) Solve the IVP: y" + 2y' + 2y = 5 sin t + 5 cos t : y(0) = 1 and y'(0) = 2

A: Given initial value problem is  y''+2y'+2y=5sint+5cost, y(0)=1, y'(0)=2. Let y'=dydt=Dy and…

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Q: Find the particular solution : y" + y' + 16y = cos4x (a) yp = -4sin4x Yp =sin4x (b) %3D %3D (c) yp =…

A: The correct option is b i.e. yp=14sin4x i.e. 14sin4x is the particular solution of the differential…

Q: Eliminate the arbitrary constant for y = 3+ C, cos 3t Oy cot 3t - 3y +9 = 0 %3! O y cot 3t + 3y-9 =…

A: To eliminate the arbitary constant

Q: Find a particular solution of the equation y2y' = cosx satisfying the initial condition y(0) = 0.…

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Q: 2) x – 2y = x°cos4x 3) x = y+x³ + 3x² – 4) +x = 4cos2y dy

A: 2)  xdydx -2y = x3cos(4x)⇒ dydx -2xy = x2cos(4x)This is a linear differential equationI.F. =…

Q: Solve ", = c²u«» 0sxS1, t20 subject to u (0, t) = 0, u(1, 1) =0 for all t u (x, 0) = 0, u, (x, 0) =…

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Q: Show that xo = 0 is a regular singular point of the equation xy" – 5 - +x ) y' + 3y = 0). Determine…

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Q: Suppose we are given y₁ (x) and y2(x) (with y₁ y2), which are two different solutions of a…

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Q: 16) y"-6y'+5y= 29 cos(2/), y(0) = 3.2, y'(0) 6.2 17) y+2y'+2y 0, (0)%3D0, y'(0) 1. y'(0) 12. y(0) =…

A: see below the solution of q16 as per bertleby guideline I have to solve only the first question ,…

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Q: 2) Consider the DE: y" + 25y = 0 A) Verify that y = C₁ cos 5x + c₂ sin 5x is a solution of the given…

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Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

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Q: (9) Show that the change of variable t = ar +b transforms the equation bo(ar + b)y" + b (ar + b)y/ +…

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Q: Which differential equation is associated with the following direction field? 2 0 Oy (y-1)(y - 3)…

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Q: (y') ² + (x-2x^-½) y'+ x^-1 - x^½= 0

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the second…

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A: Make the absolute form and solve this differential equation.

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

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Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

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Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

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Q: Find the general solution of the Cauchy-Euler equation: x²y" – 3xy + y = x°, x>0.

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Q: 2. Show that the substitution z=y(1-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)yn to a…

A: The solution is given as

Q: 9. Use the method of undetermined coefficients to solve the given system sin t X' X + %3D -2 cos

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Q: day Find y, of 2+ + 6y = 51 cos 3x. ... a.) y, = - cos 3x + 4 sin 3x b.) y, = cos 3x-4 sin 3x c.) y,…

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Q: Q6: Determine a particular solution of the equation dzy +4y 4x2 cos 2x dx2 Using D-operator method

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Q: - Second order : non- homogeneous Equations with Constant Coefficients d²y 4-- + 16y = 10 cos 4x dx²

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Q: Find one particular solution to the following second-order forced equation d²y dy +8 + 15y = 5…

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Q: The Soluton Curve for a differential equartion of the form an-y= 3n, passes through dy + passes. the…

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Q: Suppose that y1=e^x andy2=e^-x are two solutions of a homogeneous linear DE. Explain why y3=cosh x…

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Q: 5.Express this model of an electric circuit d²y dt² dt As a pair of first order equation +6+5y=sin…

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Q: If C, and C, are constant vectors and A is a constant scalar, show that H - e* (C1 sin Ày +C2 cos…

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Q: Find the general solution of the nonhomogeneous 2nd order ODE (Use the appropriate method) y" - 4y'…

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Q: Suppose that y1=e^x and y2=e−x are two solutions of a homogeneous linear equations. Explain why…

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Q: 4. y"+ 25y = 0; yi = cos 5x, y2 = sin 5x; y(0): y'(0) = -10 %3D %3D %3D 2x. u0)

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Q: b) 4 (€) -et cos (dt+물) cos (2dt +물) COS 3

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Q: Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C,…

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Q: 2. Solve the IVP y(3) + y" = 5 cos(2.x), y(0) = 3, y'(7) = 1, y"(0) = 0

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Q: mü + ku = 0 subject to the initial conditions u = u(0) and ù = ü(0) is given by the equation u(0) -…

A: Here is the solution of the given second order differential equation.