dy = f(x,y) = -2x + 12x2 + 8.5 dx Initial Condition: at x 0; y = 0.5 Now, get y between x = 0 to x = 2 with Ax = 0.5 a) Using Euler's method b) Using Heun's method

Q: Find F′(x).

A: Given Data The integral function is F(x)=ꭍxx+2(4t+1)dt.   Solve the given integral function,

Q: Consider the function y = f(x). f(x) = 8x1, x = -3 df (a) Find at x = -3. dx df dx = 3 (b) Find x =…

A:

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: f(x) = 4x In(x), x> 0.

A:

Q: is equal to 1)

A:

Q: Utt u(x, 0) ut (x, 0) = = = 4uxx x² + 3x

A: USIND D'ALEMBERT'S SOLUTION FOR ONE DIMENSIONAL HOMOGENOUS WAVE EQUATION ,WE HAVE

Q: df-1| For the function y = f(x) = x + 3x + 1, > 1.5, find dy (f-)'(3) = %3D

A:

Q: solve this equahon: Y' CH)= 2y Cf) CyCE) -) y (6):0

A:

Q: dy = 4x -3 and y(4) = 0. dx Find the function y(x) satisfying

A:

Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

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.