let y, and y2 be two solution for the D.E.: y" + (p'(x) x + p(x))y' + q(x)y = 0,x > 0. If W[y1, ya](x) = x* e¯*, and p(1) = 2 then p(x) = %3D %3D

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

Q: (2xy) dx + (y²-3x²) dy = 0

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: max value for y

A:

Q: V4 + 3f(x), where f(1) = 7 and f'(1) = 4, 62. If h(x) find h'(1).

A:

Q: Let r(æ) = f(g(h(x))), where h(1) = 3, g(3) = 2, h'(1) = 9, g/ (3) = –2, and f'(2) = 5. Find " (1).…

A:

Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: 4) (e* + y)dx+ (2y + x)dy = 0 %3D

A: Hence, the general solution is                                            y=-x±x2-4(ex-C)2 Where C…

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A:

Q: f(x)= (x+2)² (x - 1) f'(x) = 3x(x+2) %3D f"(x) = 6x +6 %3D

A:

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

A:

Q: 2) (x² – 1)y' + 2y = (x + 1)²

A: Solve the following

Q: 1. Find y' by implicit differėntiation. xy + 4x + 5x² = 3 %3D Select the correct answer: a. y':…

A: In implicit differentiation write y' interns of x & y.

Q: (2) y(x2 + y2 – 1)dx + x(x² + y² + 1)dy = 0

A: Dear Student According to Bartley by guidelines we can answer only one question at a time. Please…

Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: 5. (1-x) (dy/dx) + xy = xy". Ans. cy=(1-y)√(1-x)

A: Given equation is 1-x2dydx+xy=xy2. To find: solution of the given equation.

Q: Find yy as a function of x if y′′′−7y′′+12y′=6e^x y(0)=30,  y′(0)=19,  y′′(0)=12

A: y′′′−7y′′+12y′=6ex        y(0)=30,  y′(0)=19,  y′′(0)=12 given differential equations is linear…

Q: Let h(x) where f(x) = In(3x² + 2x + 2) and g(x) = -2x. What is h'(x)?

A:

Q: 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x) | |

A: See 2nd step

Q: Find y as a function of x if y(0) = 13, y' (0) = 22, y" (0) = 27. y(x) = y" - 15y" +56y' = 42e*,

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Q: y (2 xy +1)= xy'

A:

Q: of y = 2 tan x 1-tan²x

A: Solution is done in step 2

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

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

Q: 27. (x2 + 2x + y) dx + (3x²y -x) dy = 0

A:

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

A:

Q: (iї) Зx' — 6х %3Dsin2t x(0) = 1 (iv) у" + 6у' + 13у %3D 0 У (0) %3 3, у'(0) 3 7

A: We have to find first complementary function and   particular integral and then add them, that will…

Q: (x² + y² + x) dx + xycy = ax 0

A: The Solution is given below

Q: Find a solution of x = y²_ (a) (0, 1) 1 1-xec y = (b) y = dy dx (0, 0) y = (c) (-1/2-1/2) (d) (2,…

A:

Q: Find y' (x) if (3xy +7)² = 6y.

A: Differentiate both sides with respect to x and by using the formula for derivative of square of…

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.