Which of the following equations can be reduced to the homogenuous linear differential equation with constant coefficient? d'y dy 32 dz dz? dz Ob. 23 dz d'y dy 3z2 dz? da Oc d'y d'y dy 372 da Od. 272 dr3 dy dz? de O e d'y 22 dz dy dz2 dr

Q: 2y (y² - x) dy dx

A: We know that for the differential equation  Mdx+Ndy=0 if 1M∂M∂y-∂N∂x=fy then the integrating…

Q: Which of the following equations are linear ordinary differential equations? 1. 7x² + yx = 0 2. 7x'…

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Q: d²y dy d³y dx + a1' dx² + aoy = 0 dx + az° x³

A: Let y=eλxGiven: The differential equation:a3d3ydx3+a2d2ydx2+a1dydx+a0y=0To show: y is the solution…

Q: 1. The equation d'x _ ô²x¸ ð°x dy dwy' əw = 3 has the dependent variable x and independent variables…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Q1 Use the hypothesis V= y² and U=X To Solve the differential. equation (2x²+²-7) x dx (3X² +…

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Q: The complementary function of the differential equation d²y dx² 2 + 3x +y= dy dx 1 is (1-x)²

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Q: 4 j³g du³ + use Here equation. J J du² Sympy dy jn - y = o solve the differential

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Q: Let y = (x² + 5)5. Find the differential dy when x = 3 and dx = 0.5 Find the differential dy when x…

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Q: What is the order of the differential equation M – R()* = (#)' ds dt? dS sin St? dr2 dr

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Q: Evaluate the following. Show your solution 1. S5V dx. 3x² – 2x + 1 dr. 2. 3. SxV3x dx. SxV3x dx.

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Q: Q5) find the derivative 1. x = sin and y = sin+ cos if taken together, satisfy the differential…

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Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: 3. d'y 8 dy +y = sin x is The degree of the differential equation: da? da

A: The degree of the differential equation is the highest power of highest derivatve , so the degree of…

Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

A: Integrating factors are useful for solving ordinary differential equation  that can be expressed in…

Q: Let y = (x² + 5)5. Find the differential dy when x = 3 and dx = 0.5 - Find the differential dy when…

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Q: (含) 4 dy The order of the differential equation: d'y +y= 0 is_ dæ3 dx?

A: The Order of a differential equation is the power of the highest derivative. So here the highest…

Q: The integrating factor that transforms the differential equation 3y" – 6y' + Axy = 0 , into a…

A: The differential equation of the form, A(x)d2ydx2+B(x)dydx+C(x)y=0 can be transformed into a…

Q: Q1: Use differentials 3x-2 the appsorimate ay to AY from clanges when and x 2 to 2:63-

A: Given function is y=3x−2. We have to approximate ∇y when y=3x−2 and x changes from 2 to 2.03.…

Q: Find the differential of the function z=2x'y %3D

A: If z is a function of two variables defined by z=f(x,y) then the differential dz or total…

Q: Identify the differential equation solved by y = e** a) Oy" – 9y + 20y = 0 b) Oy" + 9y' – 20y = 0 с)…

A: The solution is given as

Q: Let y = V5- z. Find the differential dy whenz= 2 and dr = 0.1 %3D Find the differential dy whenz= 2…

A: y=5-x

Q: dy +y cotx = cscx is dx The integrating factor for the differential equation %3D Select one: cotx…

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Q: Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter…

A: we have been given the slope of the equation xy=x-2y,at (4,1) it can be written as  xy=x-2y

Q: The differential equation: 4 d'y (點) dy + x +y= x° is dx2 dx O Fourth order and non linear O Second…

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Q: differential equation y = C, sin(5x + C2) as its general solution. a) Oy" – 25y = 0 b) Oy" + 25y = 0…

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Q: What is the general solution to the differential equation A B C y = arcsin (esin 2) + C y =…

A: The given differential equation is:dydx=cos(x) esin xcos(y)

Q: Find a linear differential operator that annihilates the function 2x + 4xex D'(D - 6 D(D - 6) D'(D -…

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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.