f" + 3f' + (2+ )f = 0; f(x=0) = 0, ƒ(x = 1) = 0. dP, place the equation in the standard Sturm-Liouville form. a) Using e3"(f" +3f') = b) For two normalized eigenfunctions fm(x) and fn(x), state the orthogonality condition. (m and n are arbitrary integer labels.) You are not asked to solve the problem.

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Q: Find the general solution of the differential equation with the help of lablace transform

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Q: 5. y = x+ Vx + Vã %3D Vx+1 6. y = 1+Vx

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Q: 1) Find the second derivative of y = csc 2 e cot 2e %3D

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Q: 3. Write the exact differential: f(x,y)=e-y-el-

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Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

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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.