Bonus Homemerk@ Solve including Riccatí equation: dy -y+xy +1 dx ylo) =1 where a known solutrom of the DE, I, =x is and then write the solution in tems of the function. error

Q: dy/dt= y(y-0.5)(y-3)(sin(t2)-2) Determine the equilibria.

A: In this question, we Determine the equilibria. To explain why the Existence and Uniqueness theorem…

Q: Q-4: Find the mass (M), moment about x- axis ( M), moment about y - axis (M,) and center of mass (x,…

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Q: 6 cos ( 3x) dx Find the General Solution by Integrating both sides, and then solving for "y".…

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Q: Using Picard’s process of successive approximations, obtain a solution up to the fifth approximation…

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Q: B. NONHOMOGENEOUS EQUATIONS: UNDETERMINED OOEFFICIENTS 1. D?(D – 1)y = 3e* + sinx 2. (D² + D – 2)y =…

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Q: Quèstion 3 Solve the heat equation u; = 4u xx, - 00, u(x,0)=6(x-2). C. O A ux,t) == Je-4ax cos[@(x-…

A: Given heat equation is ut=4uxx. This is a non homogenous heat equation of the form ut=λuxx here λ=4.…

Q: give the acceleration a = d2s/dt2, initial velocity,and initial position of an object moving on a…

A: We know that velocity, y=dsdt and acceleration, a=dydt. We have given a=-4sin 2t. To find velocity y…

Q: xy dx + (2x² + 3y? – 20) dy = 0

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Q: y= Iry %3D y (0) = 0 Show that the Ivp has aunique 1T D-1(tッ))っ昇くt っ y<」 Solution - I

A: See the attachment

Q: using homogeneous d.e approach, solve (x^3-3xy^2)dx= (y^3-3x^2y)dy

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Q: Check the DE if it is exact or not then solve it. (If it is not exact use the method by using…

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Q: Using the autonomous equation dy/dx=f(y), how it is possible to obtain information about the…

A: Image is attached with detailed solution.

Q: du dy 5. da ycotx Csc x dr + 62.

A: See the details solution in below

Q: Using the method of variation of parameters find the general solution of the DE y" +y' tan t, 0<t<T…

A: please see the next step for solution

Q: The particular solution of PVI (x+y+3) dx + dy = 0  ,    y(0) =1

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Q: Solve using Integrating Factor by Inspection. Show Complete Solution. y^2 ( 1 − x^2 ) dx + x ( x^2y…

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Q: Test for exactness (2ysinxcosx - y + 2y?ey )dx = (x - sin?x - 4xye*y )dy %3D solve exact de,…

A: First we have to check exactness then we solve the differential equation.

Q: dy y - x* I Example 10.16. Using Runge-Kutta method of fourth order, solve with !! dx +x y(0) = 1 at…

A: If x0,yo is 1st approximation for solution of a 1st order differential equation then next…

Q: Use Frobenius method to find two independent solutions for the flowing equation around x=0. Find the…

A: answer

Q: Triple Integical пун Evaluate SS * cos(y) dz dx dy.

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: de termine the general Silut ion of The equation X(Y3-x) dx -YY X) ミ。

A: Given differential equation: xy3-xx-yy3+xdt=0............(i) Rewritng the differential equation as…

Q: which following one is cauchy-euler differantial equation? I→y'+y = sin y II → y' + 2y = sinx 38 -…

A: The solution is given as

Q: xdx+sin y ४ (vdx-xdy}=0

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Q: general solution DE Xy" +y'+xy=o Find the of on co ∞)

A: The given differential equation xy″ + y′ + xy = 0, known as Bessel’s equation of order zero, has the…

Q: the solution of the givin DE dy = t+y, y(1) = 0, dt at t= 1.2, h=0.1 Yexact = 0.2428 (find the…

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Q: (y – cos?x)dx + cosxdy = 0 %3D

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Q: de Fe dt ax 10. Solve Osxsa, 1>0 subject to the conditions %3! e (0, t) = 0 (a, t) =0 and 0(x,0) =…

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Q: pply Rayleigh-Ritz method to solve y" +y = x, 0 <r< 2, subject o boundary conditions y(0) = 0, y'(0)…

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Q: Solve using Integrating Factor by Inspection. Show Complete Solution.…

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Q: Integrating Factor by Formula b) y² cos xdx + (4 + 5ysinx)dy = 0

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Q: Solve using the differential operator D=d/dx. Use Method of Variation of Parameter [D2 - 8D + 16] y…

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Q: EQUATIONS REDUCIBLE TO LINEAR FORM e^y(dy/dx+1)=e^x

A: Given : ey(dy/dx + 1) = ex

Q: Find the integrating factor to make the equation exact. Then solve it. y(x+y+ 1)dx+ (x+ 2y)dy= 0

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Q: Test for exactness (2ysinxcosx - y + 2y?e*y )dx = (x - sin?x - 4xyey")dy %3D solve exact de,…

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Q: Integrating Factor by Formula a.) (2y²+ 2y+ 4x²)dx + (2xy + x)dy = 0 b) y²cosxdx + (4 + 5y sin…

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Q: II ACTIVITY # 8: esinx dx use N=5 SOLVE USING TRAPEZOIDAL AND SIMPSON'S RULE

A: For trapezoidal rule  h = b-anh = π-05h = π5 x 0 π5 2π5 3π5 4π5 π esin x esin 0 = 1 esinπ5 ≅…

Q: Using variable separable technique, find the general solution of dy/dx = (1+y^2)/(1+x^2

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Q: Check the DE if it is exact or not then solve it. (If it is not exact use the method by using…

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Q: Forward Euler's method with step h = 0.1, is applied to solve y' = = (-1+ aj)y(x) where j = v-1 and…

A: Given that the function y'=dydx=-1+ajyx                 1 where j=-1 and a is some positive real…

Q: siny µ(x,y) = ye is an integrating factor of ( - 2e-Xsinx)dx +( cosy+2e Xcosx. -)dy = 0 Select one:…

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Q: Exaple:-solve the second order differention equation d²x dx + 4- dt + 100x = sin(st) 4 dt2 Vse the…

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Q: Find the Darticular solution.Show the steps of desivation, with. the general solution.(L,Rb…

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Q: A solution of the equation (t cos t – sin t)x" + a'(t sin t) – x sin t = 0 is x(t) = t. Find second…

A: The given Differential equation is tcost-sintx"+x'tsint-xsint=0

Q: Q3/ Solue The Following Simul taneous equatron -y + Sin t + Cost %3D dt where x (6) = 1 ,x') =0,…

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Q: z = x+ y dy _ x+ y+2 1. Using substitution solve the equation which satisfies the condition y(1) =1.…

A: Use the given substitution to convert the homogeneous differential equation into separable form then…

Q: B2. Find the integrating factor by inspection then solve.  y(y2 + 1)dx + x(y2 - 1)dy = 0

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Q: TOPIC:EXACTD.E., LINEARD.E., INTEGRATINGFACTORS FOUND BY INSPECTION 2.Obtain the particular solution…

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Q: Use the Integrating Factor Method to solve 2y′−y=sqrt(x*e^x), y(1) = 0.  Put your solution in…

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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.