Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the equation y"-2 py' + (p² + q²)y = 0. %3D

Q: Integrate -- | cos 5xcos x a) 0.5 b) c) d) 2

A: We can use the trigonometric identity, cos A cos B=12cosA+B+cosA-B . Use the integration formulas,…

Q: 4. Show that sin(0 – ø) R2 – 2r R cos(0 – 4) + r² dø = 0. -

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Q: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

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Q: 5. Use Newton-Raphson method to find solutions accurate to within 10-2 for x - cos x = 0 on [0,…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0

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Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: x³y"+xy'+4y = cos (2 In x)

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Q: (3х' - 4х- 3) x* – x' +x² – -* dy = cos ydx – - 1- sin? y y

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Q: Find the general solution of y'=cos²xcosy

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Q: 2. Vsin 3x cos 3xdx

A: Given: I=∫sin3xcos53xdx For evaluating given integral, we substitute sin3x=t…

Q: 3- The integration of ſ cos(7x + 5).dx is: (a) cos(7x + 5) + C (b) sin(7x + 5) + C (e)극 sin(7x + 5)…

A: The given integral is, I=∫cos7x+5dx Now, substitute z=7x+5in the above integral,…

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

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

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Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

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Q: Q1: Use the Improved Euler method to find y' = cos2x + sin3x ,0<x < 1,y(0) = 1, with h = 0.25. %3D…

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Q: How can I find the particular solution of y''+36y=cos(6x)

A: How can I find the particular solution of y''+36y=cos(6x)

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

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Q: (1 + cos 7t) 2 sin 7t dt

A: Here we use u-subsitution to evaluate the integral. d(cosx)dx= -sinx

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

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Q: Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y.

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Q: 1. . Use the method of characteristics to solve the first order equation Uz – 2uy with u(x, x) =…

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Q: 8) Determine the smallest positive roet of the equation - 0.0i t sin (0.573t) -e

A: To determine the smallest root of the given of the function we will use Newton-Rapson method with…

Q: 3. Determine a root of the equation sin(x) + 3 cos(x)-2-0 Using the Secant method correct to five…

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

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

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Q: 18) * x-sin 2x ; find y" y y" cos 2x y = 7 %3D Option 3 O Option 1 y" sin 2x

A: First we find out first derivative with respect to x then we find out 2nd derivative with respect to…

Q: 2y 1 + cos 3x - 4.x + 3y sin 3.r = 0 %3D dr

A: 2y-1x+cos3xdydx+yx2-4x3+3ysin3x=0 Rewrite the above ODE in the form of Mdx+Ndy=0.…

Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: S 2z2 cos 5z dz using Integration by parts 2 2 z² cos(5z) +cos(5z) – + C> is this the correct…

A: We will evaluate the given integral in order to find the given answer is correct or not in the…

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: Find the general solution to the DE using the method of Undetermined Coefficients: y" + 9y = 2…

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Q: 4. Solve the initial value problem (cosy)y' = sin²x cosx , y(0) = Give the solution implicitly. %3D…

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Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0 %3D

A: Given, y = 7sin2x +9cos2x  We have to verify y = 7sin2x +9cos2x is a solution of y"+4y = 0

Q: 1. / cos" (2t) sin² (2t) dt

A: 1.

Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: 2. Evaluate the integral J cos (3x) sin°(3x)dx in two ways, one with u = u = cos(3x). Even though…

A: Given: Apply u-substitution method. Use two methods u=sin(3x)  and u=cos(3x)

Q: Q-4) Find the general solution of the Cauchy-Euler equation x'y"+ xy'+4y = sin(In x)

A: Solve the Cauchy Euler differential equation

Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

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: Differentiate y= e*cos (x2): y' = A -e*sin(x²) e(cos(x²) – 2 xsin(x²)) e*cos(x?) – 2 xsin(x²) D -2…

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

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: Solve the initial value DE y - ytanz = sinx, y(o) = 1 5-Cos 2x 5-Cos 3x 5-Cos 2x Cos 2x A) y = B) y…

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Q: Solve the initial value problem y′′ + 9y = cos(3x)+sin(3x) for y(0)= 2, y′(0)= 1.

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Q: Determine the general solution of (cos(x)cos(y)-cot(x))dx=(sin(x)sin(y))dy

A: Given: cos(x)cos(y)-cot(x)dx=sin(x)sin(y)dy