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.

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

A:

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

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: v = ) V In(2x-3y

A:

Q: Linearize the following nonlinear differential equations for the input equilib- rium of u-2 9+uy-u.

A: 4.

Q: Use separation of variables to solve the differential equation explicitly for u. du dt = 3 + 3u + t…

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.