1.) Obtain the general solution of the differential equation. (1 – xy)~²dx + [y²+ x²(1 – xy)-²]dy = 0 2.) Obtain the particular solution of the DE. (yexy – 2y³)dx + (xe*y – 6xy² – 2y)dy; when x = 0, y = 2.

Q: Which of the following functions are solutions of the differential equation y" - 2y' - 8y = 0? A.…

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Q: Identify the exact differential equation. O (1+ y?) dæ + (1 + 2y) dy = 0 %3D O sin 3x da + cos 3x dy…

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Q: State the order of the given ordinary differential equation. (1 – x)y" – 7xy' + 5y = cos(x)…

A: Order of differential equation: The order of the highest order derivative involved in a differential…

Q: consider the differential equation dy/dx=sin(x)/y for which the solution is y=f(x). Let f(0) = 1…

A: Given dydx=sinxy, y0=1. By variables separation,  y dy=sinx dx Integrating on both sides,

Q: Identify the linear differential equation. d'y 3 + ( – 1) + a*y = 5 + x?y = 5 dz? dr4 O 5y" + 4xy'y?…

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Consider the following differential equation.. y" - y' 30y = e6x Write the given differential…

A: We can rewrite this in the form L(y)=g(x) where L is a linear operator with constant coefficients.…

Q: 1. Given the differential equation: y" = cos(5x). Determine its general solution. A. 125y = -cos(5x)…

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Q: 1. (6x + f²)dx + f(2x – 3f)df = 0 2. (cos2f – 3x²f?)dx = (-cos2f + 2x sin2f + 2x³f)df 3. (fe*f –…

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Q: dy = y + x tan 2 dx is: a. sin (y/x) = cx sin (y/x) = x +c O c. y = arcsin(cx С. d. None sin (x/y) =…

A: Given that  xdydx=y+xtan(yx) Simplify the O.D.E dydx=yx+tanyx Homogeneous ODE let y=vx and solve he…

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.