Q3/ Find length of the cardioid r=a03from 0 = 0 to 0 = t %3D

Q: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

A: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: Q3\ using Euler method, find an approximate value of y corresponding to x€ [0 -0.7], Given = x(x +…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 10 In(x) dx,n = 6

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 4 10 In(x) dx, n = 6

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Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: FIND 2 DIFFERENT (LINEARLY INDE PENDENT) POR THE D.E. SOLUTIONS y"_x² y'- 3xy = o 2.

A: The linear homogeneous ordinary differential equation has the form pxy'' +qxy' +rxy=0. If the…

Q: Gixen dw wt 3y x dt dy +2X +3 x Find the gencral oludtii, usri eign.

A: Write the given system into matrix equation as follows.

Q: Exercise: Find dy O y = lox +3 Cost ® y =cscx- 4 Vx +7 Cotx 1+ Cotx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dx Evaluate J, +6x+10 by dividing the interval into 8 equal parts by using Trapezoidal rule.

A: The integral ∫15dxx2+6x+10. We have to evaluate this integral by dividing the interval into 8 equal…

Q: Use Euler's method to estimate y(0.02) ey-x y' 1 + e²y ,y(0) = 4

A: Given differential equation is y'=ey-x1+e2y with the initial condition  y0=4 and step size is…

Q: dx + AIX y = cos x, y(n) = 0

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Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

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Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

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Q: 5. (x2 + y² + 1)dx + x(x – 2y)dy = 0, x = 2,y = 3 %3D

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Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: Using Trapezoidal method √√x dx for n = 4 is equal to Blank 1 (use 2 decimal places with proper…

A: We need to use here, the trapezoidal rule.  ∫ydx = h/2 [ y0 + y4 + 2 ( y1 + y2 + y3 ) ]  For this…

Q: The distribution of P(x,y) on a thin metal plate is given by ²P 2- dx2 = 0 ду? If we use a step size…

A: Given: Distribution of Px,y on a thin metal plate is, 2∂2P∂x2+∂2P∂y2=0 Step size: h=14, k=12   To…

Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

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Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: Q1/ of xy = X+ Coty %3D

A: Given xy=x+coty  We need to find dy/dx of given equation.

Q: Q.2 Evaluate dx. (i) Using Trapezoidal rule by takingh = 0.2, h = 0.5 & h = 0.25. %3D %3D

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Q: The approximation of x'e"dx by Gaussian Quadrature with n=2 is (Use c21 = C22 =1 and r21= r22

A: Given :                 I = ∫01xeexdx

Q: 4. x(x² – y² – x)dx – y(x² – y²)dy = 0, y(2) = 0

A: For the solution follow the next step.

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: 4. Using homogenous D.E approach, solve (x³ – Зху?)dx %3D (у3 — 3x2у)dy. (v³ – 3x²y)dy. | 2 (ardai…

A: The given differential equation is; (x3-3xy2)dx=(y3-3x2y)dy.

Q: B) Find Sx e2x dx, at h = 0.2, use Simpson's 1/3 rule. J0.4

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Q: S(r* +x )dx Approximate with n = 4 using Simpson's Rule Trapezoid Rule.

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Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

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Q: Q3/ Evaluate 2 vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

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Q: Q3\ using Euler method, find an approximate value of y corresponding to X€ [0 -0.7], Given = x(x +…

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Q: Q: Approximate: 4 dx 1 - 2 Using: 1- Trapezoidal Rule (4 subintervals) 2- Simpson's Rule (n=8)

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Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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Q: 1. y(x³ – y)dx – x(x³ + y)dy = 0

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Q: 1 y" – 2y' + 2y y(4) = 0, 3 (4) = 0. -

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: Q2) Evaluate , S2 xsiny? dy dx 0 Jx2

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Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

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Q: y"+y = e" what is the nonhomogenous(particular) solution of the given differantial equation?

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Q: Q3/ Evaluate Sz Vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

A: 3 Given integral is ∫0π2sinxdx. i We have to evaluate the given integral by using trapezoidal rule.…

Q: uct Theorem. 10. K y KM=

A: Solution

Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)

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.