Solve the differential equation 1. æ°y" – 2x² y" + 6xy' = x(2ln x +1). 3

Q: au au = xt at (x > 0,t > 0) ax u(0, t) = 0 u(x,0) = 0

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Q: Solve the differential equation dy da - y²+7xy+16x² x² a. x + y = O b. x Y = ; when x = 1, y = 1 5…

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Q: (test for exactness) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xyev" )dy %3D

A: Given DE is 2ysinxcosx-y+2y2exy2dx=x-sin2x-4xyexy2dy Test the exactness of the given DE.

Q: Solve the differential equation below by undetermined coefficients: y" + 2y' = x + e²x

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Q: solve the differential equation y′′ + y = 4 cos(t)

A: solve the differential equation y′′ + y =4cos(t)

Q: Solve the differential equation xy? ; /1+ x² dy y(0) = 4 dx There is no need to isolate y.

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Q: Solve the differential equation by undetermined coefficients y" – y' = -3 а.

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Q: 9. Solve the differential equation dy/dx = 6e(²x - y) when x=0 when y = 0. a. ey=3e2x-3 b.…

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Q: Solve the following differential equation Select one: O a. yos=e"(tanx+c) O b. yos=e"(cotx+c) O…

A: Given differential equation is dydx-2xy=x2sec2x. We have to find the general solution of this…

Q: 2. Solve the differential equation- + x, with y(1) = 1.

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Q: Solve the differential equation e'y (x+2) (x²–1) * dx

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Q: Solve the ff. ordinary differential equation dy dx sin (x + y)

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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.