(D² + 1)y = 12 cos²x

Q: 1. y = c1e-2x + cze²x + cze2x 2. y = c1e* + cze3x

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Q: x² y' - 2lnx - e2y+4(Inx)/x = 0

A: Given: The given differential equation is x2y'-2lnx-e2y+4lnxx=0

Q: "-y = x e* Cos?x

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Q: 5. у" — Зу" + 2у - 1+ e

A: The given DE is: y'''-3y''+2y'=ex1+e-x⇒y'''-3y''+2y'=e2xex+1 So, for the complementary solution…

Q: dy - 2y + 6 Find the solution of the differential equation. - dx 2.x + y + 2 ||

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Q: (2xy + x)dy – [x² + y² + y + 1]dx = 0 When:x = 1; y = 0

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Q: d²y dy e* - 2 + 2y = dx² dx cos(x)

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Q: (d) (x2 + y²) dx – 2xydy = 0 (e) y' + 2xy = 10x (f) (y – 1) sin xdx – dy = 0 -

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Q: (5y – 6x)dx + rdy = 0

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Q: y(3) + y" – 2y = xe¬*

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Q: Find the general solution of the differential equation.

A: According to the given information it is required to solve the given differential equation:…

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.