What is the solution of given initial value problem? =y + sin t dt2 da + cost dt - dt2 * (0) = 1, a (0) = 0, 3(0) = -1, 3 (0) = -1 a. (t) = sin t, y(t) = – cost - sint O b. * (t) = sin t, y(t) = cost + sin t O c. (t) = cost, y(t) = cost - sin t O d. « (t) = cost, y(t) = cost - sin t O e. * (t) = cost, y(t) = - cos t + sin t

Q: dx Determine x = f(t) for (t + 7t) = 7x+ 7, t> 0; f(1) = 6. dt

A:

Q: Jo 8-7. Find the derivative of the functions: (a) h(x) = | In(t) dt g(x) = [" (c) dz 24 +1 3r (b)…

A: Solution: The objective is to find the derivative of the given function

Q: Dy/dy=x^2-y^2/2xy.     Y(1)=0

A: Given that: dydx=x2-y22xy and y(1)=0

Q: Partial solution of (4 + sine") y=e" (Grec^e^-yease") ;y (in) = 24

A:

Q: Solve "-4y + 4y = con t w(0) =1 lv(0) = 1. " sint +cont-int vit)- v(t) = ce' cos 2t + cge" sin 21 +…

A: I am matching with particular integral. But no matching option is found

Q: dy/dx= (6x^3-1)/(2xy-3x), y(1)= -1, x>0 Please show steps clearly, this is a seperable equation…

A:

Q: Question 2 Determine the general solution. x (dy/dx) = 2 - 4x^3. O y=lnx-(1/3) x^2 + c Oy=2…

A:

Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

Q: -x-1 a) y' = +2yi-1 v(0)=1

A:

Q: a) Find the particular antiderivative that satisfies the following conditions:…

A: dxdt=8et-3x0=5

Q: newton's method

A:

Q: Can you give the interval of the solution as a Bernoulli Equation?  y(0)=1 ie...  y'+p(x)y=g(x)y^n…

A:

Q: What is exact solution for dy/dx =(x2+y2)/(x+y)

A: Given: The given equation is dydx=(x2+y2)x+y

Q: (1+ 2e*/»)dx + 2e*ly (1–) dy = 0

A: Given the differential equation as (1+2ex/y)dx +2ex/y1-xydy = 0 It can be rewritten as (1+2ex/y)dx =…

Q: 3 Parameterize y(x) = +1 using x = t sin x Ans=

A: The answer is: y(t) = (-3/sin(-3/sinx) + 1)) + 1Explanation:To answer this question, you just have…

Q: Solve dy dx Option 1 - y tan x = -y² secx 1- y = sec² x + tan x + C 3- y = secx + tan² x + C 2 y-¹…

A:

Q: (1) Find y' (or 2 if y = 1+2 + V3 + v5x? + 7. (or ) dx

A: Given: y=1+2+3+5x2+7

Q: The following sentences is quantificationally true. Explain why. [(∀x)Fx ∨(∀x)Gx] ⊃(∀x)(Fx ∨Gx)

A:

Q: The equation of the tangent line to f(r) = at z = 1 is y = ar +b and the tangent point is (1, c).

A:

Q: y(1-x^2) dy/dx=x(1+y^2) solution of first order Deferential Equation

A: We have to find solution of y(1-x2)dydx=x(1+y2)

Q: y" + y = sec (x)

A:

Q: find dy/dx x(х+1)(х- 2) (х*+1)(2х+3) 25) у%3 43) у%3D 1+(lin x)? 1+(ln x)?

A:

Q: e function f m (0,0) to

A:

Q: Using variable separable technique, find the general solution of dy/dx = (1+y^2)/(1+x^2

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.