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: Solve y (e* + Inx) dx + (3 – y) dy = 0

A: The given ordinary differential equation can be written as:

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: y = x"^, x > 0 Inx-1 Inx Inx C. y'= 2lnx x' „Inx-1 D. y'= 2lnx x" „Inx-1 A. y'= x B. y'= 2 x'

A: SOLUTION-

Q: Find g'(5) given that f(5) = - 5 and f' (5) = 10. Enter the exact answers. (a) g(x) = 6x² – 5f(x)…

A:

Q: (15) y "'+ y " =e (16) y () – y (4) = 1 %3D

A:

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: Solve for y(x):  y’’ – 5y’ + 12y = 0; y(2) = 0; y’(2) = -4

A:

Q: Find g' (8) given that f(8) = – 3 andf 8) = 6. %3D

A:

Q: 2xy y' 2 =x-2 x-4 4.

A: Given y'-2xyx2-4=x-2

Q: y' = {] 4-6 3-2 y, y(0) = 5 [5 2

A: y'=4-63-2yy0=52

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: y' = (1 − x²)²; y(15) = 149,645

A: differential equation

Q: 2x³y' = y(y² + 3x²) a. y-2x2 -x +c b. yx3 -x + c C. y2x x3 -x+c d. y'x2 = -x +c

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: 2. (x2) y = y+2(x2)

A: Topic = Differential equation

Q: Find g' (3) given that f(3) = - 5 and f' (3) = 10. %3D Enter the exact answers. (a) g(x) = 4x² –…

A:

Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

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: xy y' = x² + y² %3D with y(1) = -4, then y(e)

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) ,…

Q: If g(x) = f(x² + 9x) and f'(10) = 3 , %3D %3D then g'(1) = (A) 11 (B) 3 (C) 33 (D) 29 (E) 87 (A) (B)

A:

Q: (xy^2 - x^3) + (yx^2 - y) y' = 0, y(0) = 1, solve for y when x = 2

A: Exact differential equation problems

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.