x€ (0,+) defined in the range dx +6 -+9y= of the differential equation; dx a) Write the type and rank. b) Identify the roots of the characteristic equation of the differential equation and write the general solution of the homogeneous part from them. c) Find a particular solution that satisfies the right-hand side of the differential equation above and write the general solution of the differential equation in question.

Q: y = C, cos 3x - C sin(-3x)

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Q: solve the differential equation using variation of parameters: 2x2y′′ + 5xy′ + 9y = -x2 - 2x. only…

A: The given problem is to find the solution for the given differential equation by using the variation…

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Q: Solve for Linear Differential Equation of Order n: x^2y′′+(y′)^2−2xy′=0

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Q: 3 dw + xy + w = k dx2 2 +s + 2st = 0 dx (尚) ds dt dt y" – 5x(y')2 = e* + 1

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Q: Solve the Differential Equations by Inspection (40xy-21y*)dx– (35xy³-20x²+20x?y-14xy*)dy=D0

A: The given differential equation is: 40xy-21y4dx-35xy3-20x2+20x2y-14xy4dy=0   …* Here  M=40xy-21y4…

Q: Find the differential equation by eliminating the arbitrary constants of the family of curves y = C₁…

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Q: 2 (x² + y² + 1) dx + x (x - 2y) dy =

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Q: d³u 2 dr5 d*u - 7- dr4 + 12 d³u dr3

A: The differential equation is given 2d5udr5-7d4udr4+12d3udr3+8d2udr2=0. Here ,s=ddr then equation…

Q: Form the differential equation by eliminating the arbitrary constants y = a csc x + b cot a

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Q: Solve the differential equation: *=- 6x? + 2 with initial conditions (1, 10 ).

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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.