Question 4 Solve the following equations using the appropriate substitutions (a) = 5y + ey. (b) rdy = y(ln r- In y)dr, y(1) = 4, r > 0.

Q: alculate the first six iterates for the equation x = e. When xo 0.

A:

Q: Find all solutions of y" = ln x

A: We have to the differential equation.

Q: Solve of the following Clairaut equation y=((x+4)y')+(y')^2

A:

Q: + ¹² = 4t, where y'(1) = 1 and y(1)=2. 4) Solve y" +

A:

Q: Solve the following DE: y" = 3[(y)² + 1]

A: Differential equation

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

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

Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

Q: Solve cosh(z)=1/2

A:

Q: If y = (1/2x)(sin(lnx)-cos(lnx)), find dy/dx.

A:

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

A: Given:- 2x+3y'=y+2x+31/2

Q: At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000…

A: We will find out the required values.

Q: B) Solve the following equations: y=l+x+e="x

A: We have to find the general solution of the differential equation d3ydx3+27y=1+x+e-7x .

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.