10. A fundamental set of solutions of x' = 3

Q: 2. Evaluate the integral ſcos (3x) sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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Q: Find a general solution of each reducible second-order differ- ential equation y" + (y')² = yy'

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Q: 6 The non lin ear SYStem 2 2 5 x, - X2 =0 » Xx-Q.25(Sin X, + cCos X2)=0 has solution near

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Q: Find general Solution of DE =0 on Co, mo). AISO how that xJú (x)-VJ,(x) + x Cn)

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Q: 1. Find the general solution of y'= cos²xcosy

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Q: 9. Use the Secant method to find an approximation to the solution of sin(x) - e-* = 0 in [0, 1]…

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Q: 5. S 11 sin ( 4x – 6y) cos ( 6x – 4y) dy - -

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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: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: x³y"+xy'+4y = cos (2 In x)

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Q: Q#( 1b Compute: [cos (10x)sin²(10x)dx 1 sin°(10x) – A) 30 1 sin°(10x)+C 50 1 cos°(10x)- 1 -cos…

A: We have to solve the given indefinite integral

Q: 6. Find all the values of z satisfying sinh z = = -j1.

A: What is Hyperbolic Function: The hyperbolic functions in mathematics are comparable to the…

Q: 5. Find two solutions (not multiples of each other) of the Bessel equation of order x*y" +xy' + (x²…

A: The general form of the Bessel equation is ,                                          x2y" +xy'…

Q: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

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Q: 1. ƒ(x)=x²- = x² - secx 2. w = ex²-x² + 4x 3. h(z)=In(2z)sin(2z) 3x² 4. y= √x² +1 5. y³ + 2xy = 3

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Q: (1+cos(4t) dt 2

A: Let's find integration of given function.

Q: 15. sin(2t + 글) dt = e2t-3 8. 7 4 7 64e3 7 4

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Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

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Q: Find a general solution of each reducible second-order differ- ential equation y" = 2y(y')3

A: Given the differential equation:

Q: Find the general solution to 2- ди u = xt + x cos t + t sin x. 3 - -

A: Given: 2∂u∂t-3∂u∂x-u=xt+x cos t+t sin x

Q: 12. Show that the equation z + iz + 1 = 0 has neither a real root nor a purely imaginary root.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 12. Verify by direct substitution that Un(x, y) = sin nx sinh ny is a solution of Uxx + Uyy 0 for…

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Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

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Q: 4. Solve the Cauchy problem Utt = 9uxx+cos x, (x, t) E Rx (0, ∞) u(x,0)=0, TER u(a,0)=0, x ER using…

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Q: 7). Suppose a is a positive constant less than T. Prove that the equation 2x+cos x = a has a real…

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Q: 5. Find the general solution to the DE using the method of Undetermined Coetficients: y" + 9y = 2…

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Q: b) Show that the ode (x + tan-¹ y) dx + x+y dy = 0 is exact, then find the general solution and 1+y²…

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Q: 1. Solve the DE: (cos y- cos x)y' +cos y sin 2x = 0

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Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

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

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Q: (e²)(sin²2x) Compute In y and In 5z

A: Basic log formula are applied to solve the question.

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: 4) One of the solution of the equation y"(x) + p(x)y' (x) + q(x)y(x) = 0 is given by yı (x) =…

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Q: 4.Find two solutions (not multiples of each other) of the Bessel equation of order 3232…

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Q: 11. y = x² sin x + 2x cos x – 2 sin x 12. y = x² cos x 2x sin x – 2 cos x - -

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Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: (9) Verify that Yp = sin 2x is a solution of y"– y = -5 sin 2r and use it to find the general…

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Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: Ti Ti to 8 Integrate cosh(4z) dz, C any path from - 8 Use the first method, if it applies, or use…

A: Using:- sinhx = -isin(ix)               Sin(-x)=-sinx               Sin (pi/2)=1

Q: 4. Find all solutions to the equation 4sin x cos x = v2 in the interval [0,2]

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Q: 9 Solve: Solve Sut subject to + bux = 0 u(x,0) = +x² зик + 2х их = 0 subject to ✓****/ Rx [0,00) ản…

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Q: 2. Solve Un Uxx X> 0,t> 0 with initial and boundary conditions given as u(x,0) = 1- exp(-x), u(x,0)…

A: The D'Alembert's solution of one dimensional wave equation whose charactertics lines are ξ0=x-ct and…

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

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Q: 6. x sec x tan x dx

A: Let's find.

Q: (12) Show that the Initial Value Problem S lu(x)| = 1 rE (-1,1) u(x) = 0 r= -1,1 has no (classical)…

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Q: find the 2 first non-zero of the inihiall value problem terms of the solu h'on x² y" +Clt x)y'+…

A: We find the first two non zero terms of the solution of the given initial value problem by power…

Q: 4 Give the general solution to x²y' + xy = -2 cos(2x) y¯2

A: The solution is given as

Q: 1. Use the method of reduction of order to find a second solution y2(x) and a particular solution…

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Q: 2. Find the solution set on [0, 2n). sin²(x) + cos² (;) – : -2 =0

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