x' = -2x + 4y y'= 4x - 5y x (0) = 1 y(0) = 3 %3D Δt - 0.1 Use the Euler method with a time step of 0.1 to estimate x(0.3) Use at least 5 decimal places in your calculations.

Q: 7. y - y = 16

A: The objective is to find the general solution .

Q: x² – 16- vx2 – 16 8ln (x + %3D 112

A:

Q: If y = 2x*- x², find the values of x for which y' = 0. %3D

A: Differentiate wrt x and put zero

Q: c. y = V6x2 +1 с. Rewrite y = y'=

A: we solve this differentiation by using chain rule

Q: y' = et ; y(0) = 2 find the general solution

A:

Q: Solve the D.E y' 1 (e-y-x)

A:

Q: 2 (x-4) dx = (S %3D 2.

A: Given : The definite integral is ∫02 ( x - 4 )2 dx .

Q: Solve: у" + 5у'" — 2y' - 24у — 42е 5t 2y' — 24у 3D 42e — 2, у'(0) — — 6, у'"(0) —D — 30 | | | y(t) =

A:

Q: Find dy/dx if y = e-(1/10)e-x/2.

A: Given: y=e-110e-x2. To find dydx. Solution: Chain rule of differentiation states that:…

Q: Find y' for y = 7x-3+ 5x - 1

A:

Q: here is Colon Cancer New Cases 2017 y1=2609.58x2-971041 corr(x2y1)=0.988  what does it tell you…

A: The regression equation and correlation coefficient are given. We have to describe those values.…

Q: Solution: y1 = 1.450000000; y2= 2:085625000; y3 = 3:079099746

A: Here, initial condition is given at x = 2.Therefore, start with x0 = 2.Given equation is:

Q: Approximate y(0.8) in the function y' = x - 2y when y(0) = 0, x(0) = 0 and the stepsize is 0.2 using…

A:

Q: 3. Find all of the equation. (а) у —х (c) y' = x Inx (e) y" = 2xe*

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter…

A: we have been given the slope of the equation xy=x-2y,at (4,1) it can be written as  xy=x-2y

Q: Find y' and y". - in(x + V6+ x²) y = In( x + y' = y" %3D

A: Given

Q: x' = 10 t² x², x(0) = 3 Solve the above IVP and then find x(0.5). Put x(0.5) accurately calculated…

A: Given differential equation is, x'=10t2x2, x0=3.

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: y= x2/5 Local extrema

A:

Q: solve dx dt. (1 = 72 X -2 7 with X (0) = 3 L2

A:

Q: solve y’ – (y/x) = xy2

A: We have to solve differential equations

Q: Calculate the first, second, and third derivatives of y(t) = 2016/5 – 6127. (Use symbolic notation…

A: We will use simple differentiation rules to solve this question.

Q: Find y' for y=8x7 + 4x¯¹. 1 y'=0

A:

Q: Runge-Kutta 4th

A: y' = y-x   , y(0) =2here h = 0.1f(x , y ) = y-xx0=0y0= 2y(0.1) = y(0) +16(k1+2k2+2k3+k4)k1 = (0.1)…

Q: (c) y" – y' = t², y(0) = y'(0) = 0.

A:

Q: Solve for y. y' = 7x + xy​; y = - 4 when x = 0

A: Given,  y'=7x+xy,  y=-4 when x=0

Q: Use Euler method to approximate the value of y(0.2), given               ay' - by = ce^(kx) + mx  ,…

A:

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

A:

Q: y' - 5 y = 5e3¤ for y(0) = 5 %3D

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.