2. Use separation of variables to solve (a) y' = -2y, y(0) = 1 (b) 4y' = y², y(0) = 4 %3D (c) y' + y = 0, y(0) = 2

Q: y = V In(5x + 7)

A: In this question, we use the chain rule to find the derivative of the function .

Q: If f' (4) = -9 and g ' (4) = -5, find (a) h'(4), if h(x) = 10f(x) + 2. %3D h'(4) = %3D (b) F'(4), if…

A: Recall: (αf(x)±βg(x))' = α f'(x)±β g'(x) ; where α and β are real numbers.

Q: Solve y" +5y' = (2x+1)e" -5x

A:

Q: Suppose that f(2) = -3, g(2) = 2, f '(2) = -4, and g'(2) = 5. Fir (a) h(x) = 5f(x) – 4g(x) h'(2) =…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

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

A:

Q: f(x) = 8x-1 %3D f '(x) = %3D

A:

Q: Find y'. y = V In(7x + 5) y' =

A: Given the function y=ln(7x+5)         ........(1)

Q: y'-(2/x)y=(y^3)/(x^2) find the solution that satisfies y(1)=1

A: The given differential equation is

Q: Solve y'' + 9y = 8(t – 2), y(0) = y'(0) = 0 y(t) = for t 2

A:

Q: f" (x) = 5x + 6 and f'(-2) = 1 and f(-2) = 0. Find f' (x) = and find f(2) =

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: Solve y' = (y − 1)(y + 1) for y(0) = 3.

A:

Q: 8) y'+y=17 sin(2t), y(0) =-1.

A:

Q: Solve for y. y' = 7x + xy; y = 5 when x= 0 y =

A: We have to solve for y for the given differential equation: y'=7x+xy; y=5 when x=0. Rewriting the…

Q: G(y) = (y − 1)4 / (y2 + 2y)7 Find G'(y) =

A: for a polynomial function of power n: Division rule of differentiation:         Chain rule :…

Q: y' = = x/n(x)

A: We can find the derivative of the given function by using logarithmic differentiation.

Q: - 1 Find y' for y=7x7 + 9x¯ y' =

A:

Q: 3. Solve y'" + 6 y' + 9 y = 0, y(0) = 5, y'(0) = - 8 %3D %3D y (t)

A:

Q: If f' (2) = -5 and g'(2) = 3, find %3D (a) h'(2), if h(x) = 12f(x) + 4. %3D h' (2) = (b) F'(2), if…

A:

Q: Solve 5 2 E #(0) = – 2, y(0) = = 10 | Ly' - 29 - x(t) = %3D y(t) =

A:

Q: solve: y'' - 5y' + 4y = 20cos(2x) + 30sin(2x) y(0) = 1 y'(0) = 3

A: We have to solve the differential equation given below : y'' - 5y' + 4y = 20cos(2x) + 30sin(2x) ,…

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.