An ordinary differential equation of a horizontal string which is freely pinned at both ends is given by d²y a²y W P (x² – lx), where a² EI dx? 2EI Find the deflection of the string at any point.

Q: Find all solutions of y" = ln x

A: We have to the differential equation.

Q: x(2y – 3)dx + (x2 + 1)dy = 0

A:

Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: ion C(x)=10x+700 are produced. Find the  fixed co

A:

Q: Find the first derivative: y= In V5x3 - 2

A: Given: y=ln5x3-25 We need to evaluate dy/dx. This can be done as follows:

Q: Find the differential equation of the following families of curves: y2(b+x)=x2(3b-x)

A: Given y2(b+x) = x2(3b-x)                 (1) Differentiate equation (1) with respect to x , we get…

Q: Solve the following Clairaut equation   y=xy'+(y')^2

A: Firstly we will differentiate this equation to get simpler differential equation

Q: b.) y = x²ln (2x + 3)

A:

Q: Find the differential of the function. p = 39 - 893/2 dp =

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.