3. (D² + 1)y = 0

Q: Find the solution of (x-2)dy = (3x² - 6x - y)dx given y(0) = 4.

A:

Q: dy ニ 3 x +y-2

A:

Q: 32 8y%dy y-15 2.

A: The given integral is,

Q: d, 3 Find dx -)- + x(х - 1)). A -3 +2х-1 B +1 -3 +1 -6 +2х-1 x3 (D

A:

Q: d²y dx² - dy - - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

A:

Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: 9-y" - 2y +2y=e; y(0) = 0, y(0) = 1

A:

Q: y = x(2x+1), y" y = (4x − 3)¹/²2, d³ y dx³

A: Topic:- derivatives  Note :- as per our guideline if more than one question uploaded than only first…

Q: Find ax dy x-2–1 given y = 2x3

A:

Q: Evaluate the integrals

A: To evaluate, ∫01∫03-3x∫03-3x-ydzdydx

Q: (4x-3) find dy/dх y = (2х-7)6

A:

Q: calculate d2y/dx2 when y=3/x

A:

Q: calculate d2y/dx2 when y=-3x2+2x

A: . Given y=3x2+2xwe find d2ydx2

Q: = -21e 2 C D +4 D +9D t1o)y 4. /f x-O -4 l 10

A: To sove the initial value problem for y=y(x)

Q: ) y( 3x*- xy - 7)d -x ( xy ty- 2x) dgy = 0

A:

Q: z· 3°dz

A:

Q: B: Find dy /dx 4x5-5x+2x3 2- y = x2

A: We have to find the derivative dy/dx.

Q: - 15x + 14x +2 dy DA. dx - 30 – 2x = dy O B. dx 15x + 14 +2 - dy D C. = - 30x - 2x2

A: we have to find the derivative of y=-15x3+14x+2x

Q: Find d2y/dx2 for the equation x=x3y2-3y3

A:

Q: Calculate (ay² + y) dy dæ. 3.

A: We use the properties of integrals to evaluate the given integral.

Q: (x² + y²)dy dx 7.

A: Given  ∫-22∫04-x2(x2+y2) dydx

Q: d'y d²y dy dx3 -2 dx2 +9. - 18y = 0 dx

A: Given equation is d3ydx3-2d2ydx2+9dydx-18y=0Here we have a linear differential equation which…

Q: -dy (49 – y2 )

A:

Q: calculate d2y/dx2 when y=0.4x-0.3

A: use this formula:

Q: Find d2y/dx2   e4y+x=8y

A:

Q: y"+ 2y' +y =e* x-

A:

Q: d'y dx +8y = 2x – 5 + 8e **, y(0)=-5, y'(0)=3. y"(0)=-4

A: Given the differential equation            y'''+8y=2x-5+8e-2x with initial conditions y(0)=-5,…

Q: If y = 2x² then dy dx 11

A:

Q: dy 4x2 + x dx y + 4

A: Given : dydx = 4x2+xy+4

Q: d³y d²y 4. dx3 dx3 dx -dy + y = 0

A: Consider the given equation. d3ydx3−d2ydx2−dydx+y=0 Now, make the characteristic equation.…

Q: G. (3x ty - 2)dx + (3x ty +4)dy <0

A:

Q: Find d2y/dx2 if y= (x2-1)(x3+2)

A:

Q: 1 S² = y e2y dy

A:

Q: у4у? -16у +19 dy (y-2)°

A: This indefinite integral can be solved by the substitution method.

Q: If y = x3 – 2x2 + 3x – 1, then d2y/dx2 is equal to

A: topic - derivatives

Q: Let y = 4**-2x+3. Find d²y - dx2°

A:

Q: 4-y² ²) dædy 2 2

A:

Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: y, = x2 + 2x + 2 Y2 = 2x + 18 dx 25- 20 15 y 10- 5- 6.

A:

Q: what is the solution of equation 2ydx + (2xlogx - xy)dy = 0

A: Given differential equation is. 2ydx+2xlogx-xydy=0

Q: dy 2 y = x3 – 6x3 бх3 — 5; - | dx5

A:

Q: In x y of y = 3

A: Find your answer below

Q: d) y" -ry +3y = 0 %3D

A: Using power series method.

Q: />(4y++ +9) * dy 12y2-

A:

Q: -2 S.f(x)dx -4 a. b.5°2f1x) dx C.5f(x) dx

A:

Q: calculate d2y/dx2 when y=-2/x2

A: Given: y=-2x2

Q: dy 3x - 4 81. if y = %3D dx 12r²

A:

Q: D’(D² – 4)y = 3x+ 2e¬3* | y = 3x + 2e¬3x m° – 5 - 4m³ = 0 ® m' (m2 – 4) = 3x+2e-3* D (D² - 4) = 0 3…

A: