Determine the general solution for following Cauchy-Euler Equatio dy + 7x +5y = x³. i) dx2

Q: 4. If integration using u-substitution technique is used to solve for correct choice for u? (a) u =…

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Q: y"-uy'+5y= e Sin() %3D

A: We have to solve given problem:

Q: Solve using Euler's Method dy dx sin(x+y) ex,y (0)-4, h-0.1 -

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Q: Solve the following DEQ by separable method: dy (cos x + 1)( sin y – 1) dx

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Q: Evaluate the integral dx (5ӕ + 10)2 by making the appropriate substitution: u = dx (5x + 10)? II

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Q: 1 To evaluate the integral dx, we (x2 + 2x)3/2 sec 0 1 substitute

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Q: Obtain the particular solution satisfying the initial condition indicated. (variable separable) dx…

A: Use the variable separable method and satisfy the initial condition. Also use the properties of…

Q: Solve the differential eqyations (3x +5y +4)dx + (5x +3y +6)dy =0

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Q: The value of the double integral 7 1 4xy dy dx is 4

A: ∫46(∫274xydy)dxIntregation wrt y so x will be constant.⇒∫46[4xy22]27dx ⇒∫462x(49-4)⇒∫462x(45)dx

Q: 1) = sinx + ytanx dy dx 2) x = y + x sin? 3) Prove that (2xy – 9x2)dx + (2y + x² + 1)dy = 0 is…

A: 1   dydx=sinx+ytanx        the equation can be written as standard form        dydx-ytanx=sinx…

Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

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Q: Show that if you differentiate both sides of x2 +2y³ = 6, the result is dy dx 2x + 6y² = 0. Then…

A: Given function is x2+2y3=6 Power rule of differentiation states that  ddxxn=nxn-1 And ddxconstant=0…

Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: SVEsin(1+ VF )dz 4 Vz sin .3

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Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: Q,7 Evaluate the integral 1) L,x* dx 2) xVx+1 dx 3) f cos2xdx

A: we have to solve

Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

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Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

Q: (3) Integrate using an appropriate substitution 2e- -d.xc e + 3 x-

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Q: Find the general solution: dy = tanxtanydx %3D

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Q: Evaluate the integral dx (8x + 3)3 by making the appropriate substitution: u = 8х + 3 dx (8x + 3)3…

A: Recall:    ∫un du=un+1n+1+c ; where c is an integration constant.

Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: 2/3–2 dx integralinin değeri x² + 4x + 8 aşağıdakilerden hangisidir?

A: The integral can be solved using completing the squares method. Since the integration is definite…

Q: solve the given nonhomogeneous ODE x^2y"-2xy'+2y=x^3sinx by varition of parametrs

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Q: Obtain the solution using Integrating Factors Found by Formulas. 2(2y2 + 5xy- 2y + 4)dx + x(2x +…

A: We can solve this using integrating factor

Q: 4. Obtain the general solution of x? y dy dx

A: By Bartleby policy I have to solve only first one as these are all unrelated problems

Q: dx · xcot2y = x³csc2y dy

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Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: 4. Compute dx S in two ways and verify that the answers agree.

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Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

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Q: Find the general solution of dy (y2 + 4) In x In(y2 + 4)"* %3D dx

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Q: Show that the DE (4y3 -6xy)dy = (3y2 +2x)dx is exact and find a solution of the IVP: (4y3 - 6xy)dy…

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Q: Determine the solution for this DE 1.) du/dx = (u2-x2) / (x2-u2 ) , u(1) = 0

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Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

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Q: Use an appropriate " Bernoulli substitution" to solve: dy + XY 4X s Y(O) =2. %3D dx ya

A: In order to solve a bernoulli's differential equation, first we have to convert it into a linear…

Q: Solve the Linear DE dy/dx = 1+ 3y tan x

A: I have stated the used formulas in the solution.

Q: (1+ In xy) dx + (-)dy = 0

A: See the attachment

Q: dx-(it 2x tany) dy-0

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Q: Solve the Euler equation d²y dx dy -5y = 0 dx 31 d', 3x2 given that y(1) =1 and y'(1) = 2. intai

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Q: 2. Test for exactness and find the complete solution of n dx + {In(2x – 2) + dy = 0 - (х-1)

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Q: ydx = x(1+ xy4)dy

A: Given ydx=x(1+xy4)dy ⇒dxdy=xy+x2y4y⇒dxdy+x-1y=x2y3

Q: Compute dx in two ways and verify that the answers agree.

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

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Q: Integrate both sides = S sec²y dy = S dx

A: ∫sec2y dy=∫dx

Q: prove using the IVT. e^x + ln x = 0 has a solution.

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Q: Solve for the general solution of the given non-exact DE. y(y + 2x – 2)dx – 2(x + y)dy = 0 - -

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Q: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

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Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu

Q: Determine the solution to this DE: * dy t By 2 dx

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.