(a) Show that the following Euler equation can be transformed into a 2nd order ODE with constant coefficients by letting x=e'. x²y" + pxy' + qy = 0. where p and q are real constants. (b) Find the general solution of the following equation where x > 0. х?у" + 5ху' + 4.25у %3D 0. ||

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A: According to Bartleby guidelines I have solved first, since this is not interrelated question,   For…

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A: To solve the given ordinary differential equation.

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A: Since you have posted multiple question in this question so I have solved first question as per our…

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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.