Question 2: Solve the following problem with the fourth-order RK method: d?y 2- dx2 dy +3 +3.125y = sin x dx where y(0) = 5 and y(0) = 3. Solve from x = 0 to 5 with h = 0.5. Find the error considering the exact solution is y(x) = e75 (5.292237 cos x + 6.859589 sin x)-0.292237 cosx +0.109589 sin x Display the analytical and numerical results on the same graph.

Q: If +a= a(2 cos 0 cos 20) and y=a(2 sin0 sin 20),show that (z² + y² + 2az) = 4a² (z² + y²). %3D

A: Given that, x+a=a2cosθ-cos2θ⋯⋯1y=a2sinθ-sin2θ⋯⋯2 Squaring both sides of (1) and (2) and adding,…

Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

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Q: If the following eq. is exact, then solve it (y cos x + 2xe) + (sin x + x²e + 2)y' 0.

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Q: The value of 52003 mod 7 is? 4 0 3 0 9 O 8 0

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Q: Solve the following equation: (X² + y²) dx = 8 (XY)dy, and find the value of y at x = 5 where y = 0…

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Q: a) Use the d'Alembert solution to solve -00 0, 9 Əx² ' x,

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Q: B) Find the general solution of the equation by using (Undetermined Coefficients method) d'y dy de =…

A: Solution of the differential equation using undetermined method

Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: Solve: (cos x) · (dy/dx) + y sin x = 2x cos2 x, y(Tt/4) = (-15/2-n2)/32.

A: The given differential equation can be written as :            dydx +ytanx = 2xcosx So, the…

Q: In order to solve with we first write and Setting to get sin 2xdx + cos 3ydy = 0 y(π/2) = π/3 cos…

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Q: cos(t) dt 2/3sqrt(x+5)^5-10(x+5)^(1/2) +C (5 sin(t) + 9)2

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Q: Q2/ If the following eq. is exact, then solve it (y cos x + 2xe") + (sin x+ x²e° + 2)y' = 0.

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: 9. Solve the equation for 0 < x S 2n: sinx + cosx = 0 10. Solve the equation for 0sxS 2n: sec?x +…

A: Given that: 9. sinx + cosx =010. sec2x+2secx=0

Q: Consider the following DE: (+y5+ y² sin x) dx + (5xy¹ - 2y cos x + e")dy = 0, where x > 0. (a) Show…

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Q: Solve. Soc 3 cos (5xx)dx

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Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

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Q: dr. r²VI+a 17 Please present the the results of the main steps of your solution in a table similar…

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Q: Solve the initial value problem. (cosx)(dy/dx)+ysinx=6xcos2x, y(pi/3)=(-4pi2/3)

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Q: Assume cos(t) = - where <t <a. Compute the following %3D cos(-t) = sin(t) = sin(-t) =U sin(-t) +…

A: topic - trigonometric ratios sin(-x)=-sin(x) cos(-x)=cos(x) sin2(x)+cox2(x)=1

Q: Question 2 Find the solution to the DE. (y-x+xycotx) dx + xdy=0 xysinx=C+ sinx - xcosx Oy=(c +…

A: Concept: For a differential equation of the form P(x,y)dx+Q(x,y)dy=0 The differential equation is…

Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

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Q: Find the solution. dy X-+ 2y = dx sin x y(2) = 1 A cy = (3 – cos 2x – tanx)/x? B x = (2 + cor2 –…

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Q: ly 3)[e^(-2y)]dy

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Q: Applying the method of undetermined coefficients, solve y" + y' + 8y = (10x² + 21x +9)sin 3.x + x…

A: Given differential equation, y''+y'+8y=10x2+21x+9sin3x+xcos3x To find the auxillary equation,…

Q: 1. Solve y' + 3x²y = cos(z)e with y(0) = -3.

A: Sol:- y' +3x2y=cosxe-x3A first order linear ODE has the form of y'x+pxy=qxy'x+px·y=qxpx=3x2,…

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.