d'y dy da 7x- + 16y = 0 da2 has r as a solution. Applying reduction order we set y2 = ux". Then (using the prime notation for the derivatives) So, plugging y2 into the left side of the differential equation, and reducing, we get x'y-7xy, + 16y2 = The reduced form has a common factor of x° which we can divide out of the equation so that we have xu" + u' = 0. Since this equation does not have any u terms in it we can make the substitution w = u' giving us the first order linear equation rw + w = 0. This equation has integrating factor for x > 0. If we use a as the constant of integration, the solution to this equation is w = Integrating to get u, and using b as our second constant of integration we have u = Finally y2 = and the general solution is

Q: Use the method of undetermined coefficients to solve the differential equa- -2x y" + 5y' + 6y = e-®…

A:

Q: Solve the given differential equation. dx/dy = -( (4y^2+10xy)/(5y^2+2x) )

A: Given DE is dxdy=-4y2+10xy5y2+2x. Solve the DE as follows.

Q: Determine whether y = 2x is a solution of the differential equation y'= 6x², a. 6x2- and by'= 6r?…

A: Just take derivative of y and substitute in given differential equation and see if it satisfies the…

Q: Solve the differential equation by variation of parameteres:   y'' + y = sin2 (x)

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Q: Please help me with this differential equation and identify P(x), Q(x) and v(x).

A: The general form of first order  linear differential equation is shown on board

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A:

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.