4. Solve the following initial value problem dy 2y dr = x='y-}, y(1) = 3.

Q: 2. y' = 4x(2y3 -y)

A: Given differential equation, y'=4x(2y-3-y)..........(i)⇒y'+4xy=8xy-3⇒y3y'+4xy4=8x...........(ii)

Q: Consider the following equation (1−2x−x^(2))y''+2(1+x)y′−2y=0

A:

Q: 3. y' = 3x? –2; y(1) = 5

A: When the linear differential equation is in the form, dydx+py=Q    ..........1 Then the solution of…

Q: 2) Solve the equation y' = Y 4x²y + x

A:

Q: 2yy" = 1 + (y')² 2

A:

Q: х? + 2х + 9y? — 18у + 11 3D 0 Is the equation of: Select one: О а. Нурerbola O b. Ellipse O c.…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 5. If y=5x²-3x + 10, give y'(-1)

A: We have to find the y'(-1).

Q: y = In (x+ v5² +1) 3. Solve the y'" if x = 0.5 using step size of 0.1

A: We approximate the second order derivative using second order central difference approximation.!

Q: Find y''' for y = 1/(x+4)3

A: To find the first derivative, y' of y, differentiate (x+4)-3 with respect to x, using the general…

Q: Determine the solution to the I.V.P. y'' + 7y' + 12y = 21e^3t , y(0) = 7/2, y'(0) = -10

A: Solution

Q: 3x²y' = x(5-6y) x = 1; y = 2

A:

Q: If y = (x+1)/(2x - root x' then y' will be?

A:

Q: 23. (1.4) Solve y +2 = (4x + 2y + 6)-'e2«+v+3.

A:

Q: If x +1 y = x - 1 then y' (3) equals (enter your answer as a decimal)

A: given y=(x+1)/(x-1) we need to find y''(3) first let us find y''(x)…

Q: 5. Solve 2y" - 3y' - 2y = 0; y(0) = 1, y'(0) = -1.

A:

Q: 5. Find y'. y = 3x² – 14x + 42

A:

Q: Find y' implicitly. 1. (x + y)² = 4y 2. (x + 2y)² = x + 10 of 1

A:

Q: . y′ = 2y y'

A: Given differential equation: We have to find the solution of the given differential equation.

Q: Solve  y'' − 2y' + 5y = x2 + 1

A: Solution

Q: find the general solution of y''+2y'-3y=(5x^2-7)e^-x

A:

Q: . y′ + 3x^2y = x2

A: Our Aim is to solve the differential equation given below:-y'+3x2y=x2 -(i)

Q: Find the solution of y''+6y'-7y=80e^(3t) with y(0)=7 and y'(0)=2 y=?

A: Differential equation.

Q: 11. Find y'if y = 2x + Vx* – 9x+3

A:

Q: Find y' if y= - 14 3 X

A:

Q: Find y' 1. y = (x3-5x2)5 2. y = 3x-1+5x2

A: The functions: 1. y=x3-5x25 2. y=3x-1+5x2

Q: ンX>0 y3

A: Given: y'+yx=5y3

Q: find the solution of y''-2y'=x - e^3x

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.