Use the d'Alembert solution to solve -00 < x < oo, t> 0, u(г,0) cos? r, u(x, 0) = e®+1.

Q: Find a solution to the euler equation, from : rx2 (2? – y/²)dx

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Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

Q: Solve the DE. If o(x) is the solution to the DE, find o( - 2) $( – y = xe- x*: (0) = 0

A: Solution of the differential equation

Q: Solve the attached equations  by the method of undeterminedcoefficients.

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Q: C3x -y sin xy) de - x sin sy dy o HSin

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Q: 6. Solve, using the method of undetermined coefficients: y" – 2y' + 2y = e²= (cos r – 3 sin z)

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Q: Solve this Di fferential equat ion by applying (Variation parameters) y+y%3DSE c x

A: The given differential equation is y''+y = sec x

Q: Show that the equation dy + 2k possesses solutions of the form E c, e cos (a,x+&,) cos (w,t+ 8,)…

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Q: Solve D.E using bernouliis equation os(y)·y' + sin(y) =x

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Q: 4. (D² + 2D + 5)y = 4e-*cos²x

A: Given differential equation is: d2ydx2+2dydx+5y=4e-xcos2x Auxiliary equation corresponding to given…

Q: x°y"+ 2x?y"+ xy'- y=0

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Q: 2. Solve dx2 d²y for x = u? + 1 and y = 3u3 – 3u in terms of the parameter u. -

A: Given query is to find indicated derivative.

Q: What is the form of a particular solution of the equation: y" – 6y' + 9y = t² + e* – 4 cos t Do not…

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Q: Solve the IVP (1/x + 2y^2x)dx + (2yx^2 - cos(y))dy = 0, y(1) = pi. Give an implicit solution.

A: Consider the differential equation 1x+2y2xdx+2yx2−cosydy=0.........(1) Compare the equation (1) with…

Q: Reduce to first order and solve 1> 2xy"= 3y' Cos n ii) xy"+ 2y'+zy = 0, Y, = ニ

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Q: Use the method of undetermined coefficients to find the general solution: y" + 4y : = cos 2t

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Q: Find the solution. (Dª+2D3 + 10D2)y =0. @y = c,e-+czxe¯+e"(e,cos3r +c,sin3x) y = (c,+c,)x+e*(c,cos3x…

A: To solve the given Differential equation.

Q: dy 5. Solve the IVP: = cos(r+ y), y(0) = dr

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Q: Solve the given DE. (D² – 3D + 2) Y 1 cos² (e¬²)

A: Differential equations, method of variation of perameters

Q: . Find the qeueral solution: - 2 dy +5y = ex Cos 2x

A: Complete solution = complementary function + particular integral.

Q: CSc x e dx Cos x

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Q: Solve linear DE  (D2+2D+2)y=e-x+sin2x

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Q: solve the equation by using Bernoulli's equations. y' + p(x)y = f(x) y ln y

A: Y’ +p(x)y =f(x)ylny divide equation with y both side we get y’ /y +p(x) = f(x) lny now consider lny…

Q: (cos t)y" + (sin t)y' – ty = 0,

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Q: Find the solution. (D2-4D +7)y = 0 y = e-2(c,cos3x +c,sin3«) Oy= e"(c,cos/Zx+c,sin/2x) O y-…

A: Given differential equation is (D2-4D+7)y = 0

Q: dy = 6x– 2x + 1 cos y + eY %D dx

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Q: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: solve linear DE (D2+2D+2)y=e-x+sin2x

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Q: Use the d'Alembert solution to solve 1 0u 9 dx2' u(x, 0) = cos? x, u(x,0) = e"+1. -0 0, t > 0,

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Q: Solve the DE (ey+1)cosx dx+eysinxdy=0

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Q: Solve the equation on the interval [0.2x). V2 cos 2x = 2n 4元 O A. 0, I 3 5x 7n O B. - 4 4 4 4 л 7л…

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Q: Finally, we substitute for u to write the answer in terms of x. Use C for the constant of…

A: ∫x3e7x4dx

Q: c) Se' sec (e - 1) dt

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Q: Obtain the general solution using Bernoulli's equation. Simplify your final ansv answer. ix- 6* dy =…

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Q: Finally, we substitute for u to write the answer in terms of x. Use C for the constant of…

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Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y +4y=x-2 cos 2x,…

A: The solution is given as

Q: Solve by Chain Rule g(t) = sin (e1-t + 3 sin(6t))

A: Solution is written in below steps.

Q: Solve for the general solution of (D: - 1)y = sinx using variation of parameters y = cje¯* + ¢ze*…

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Q: Find the General Solution (D² – 3D + 2)y = cos(e¬*)

A: We need to find the general solution of (D2-3D+2)y=cos(e-x) Note the results  ∫cosx dx=sinx+C ∫sinx…

Q: Use the method of characteristics to solve the first order equation Ug – 2uy = 3 with u(x, x) =…

A: Method of Characteristics and General Solutions: The general solution of the quasi-linear equation…

Q: :.) Solve the equation using discontinuous function: y" + 9y = cos(2t) – u47(t)cos(2t)

A: Please check step 2 for the solution.!

Q: What is the solution of D.E (D2 - 2D)y = e sinx when solved using the method of undetermined

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Q: Show that the equation + 2k dy =c². possesses solutions of the form 00 2 c, e " cos (a, x + &,) cos…

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Q: Use any method to solve the particular solution (D² + 9)y = 81x² + 14 cos 4x ; when x = 0 y = 0 y' =…

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Q: Show that the equation dy + 2k possesses solutions of the form 00 - kt E c,e cos (oa,x+ E,) cos (w,…

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Q: Using the method of changing independent variable, solve (1+ x)°y" + (1 + r)y' +y= 4 cos(In(r + 1))

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Q: Solve using method of undetermined coefficcents (D2 2D + 2) Y 24 e sin 3X when x=0, y=D0. y=0

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Q: Solve for the Bernoulli's equation -- ses 2ds = 5t³s3 .33 %3D dt

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Q: Solve the diffedential equation 2 e ys + y de ]dy-o

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Q: Solve the equations by variation of parameters. d2y/dx2 -dy/dx = ex cos x, x&gt; 0

A: d2ydx2-dydx=excosx

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.