ordinary differential equation of

Q: Problem 4 (Non-homogeneous Equations Redux). By now we are very familiar with a procedure for…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 3) yy +x²(sinx)³ = y³cotx %3D

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Q: y = e - 2x %3D sine

A: First, find the auxiliary roots from the given equation. Use yx=c1y1+c2y2 to write complementary…

Q: cosy dx + (1 + e¯*)siny dy = 0

A: By separating the variables on each side  we can integrate them easily. Given, cosy dx+(1+e-x)siny…

Q: x = c, e" + cz e- 21 e" O x"- 2x'- 3x 8 e O x" + 2r'+ 3x = 8 e' O x" - 3x'- 2r 8 e O x"- 2x'+ 3x = 8…

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Q: Find the series solu tion to the differential equation x?y" + (1 + 3x)y' + y = 0. A) y = a,(x +÷x² -…

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Q: xy² + a-2y+ 3) dæ + a ydy – 2 (x+y) dy = 0, when a = 1; y = 1 %3D

A: Given differential equation is  (xy2+x-2y+3)dx+x2ydy-2(x+y)dy=0

Q: 1. (cos 2y-3x²y²) dx + (cos 2y - 2x sin 2y - 2x³y)dy = 0 - 2. [x√x² + y² − y]dx+ (y√x² + y² − x)dy =…

A: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydx The differential equation is of the form Mdx+Ndy=0 We know the…

Q: 3. A dead body was found within a closed room of a house where the temperature was a constant 70°F.…

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Q: degree dy 6. dx = cos X d²y' dx2 2 (dx + 2b + y = 0 7. y" + (2y')2-y = 4x 8. 9. yy" + 2x3 = 0 10. y'…

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Q: Find a general solution of the differential equation: x²y" – 3xy' + 4y = 2x -

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Q: (e) y" – 4y' + 4y = 2x

A: To find the general solution

Q: y = C1+ C2cosx + C3sinx %3D

A: The given equation is, y=c1+c2cosx+c3sinx⋯⋯⋯⋯1 Differentiating with respect to x,…

Q: (D^2 +2D+2)y=e-xcscx

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Q: State the order of homogeneity and solve the differential equation as a homogeneous equation. x dy…

A: Given xdy=(x+y)dx

Q: Find the power series solution near X, =0 of the following equation (x² +1) y"- 4xy'+ 6y = 0.

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Q: dy _ху + Зx — у — 3 - - 19. dx ху — 2х + 4у — 8

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Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

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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.