Find the particular solution y" — 4y' + 5у %3D 0; y(0) = 5, y'(0) = 2

Q: y" − 4y = 10

A: The given differential equation is y" − 4y = 10. Its auxiliary equation is m2-4=0. Obtain the roots…

Q: x3y" – 5xy' + 9y = 0 -3x y" + 5y' + 4y = 10e %3D

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Q: 2y" + 29y = 0, %3D y(0) = 7, y' (0) = 7. y(t) =

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Q: find sol. y'- y =y2e-x

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Q: Find y'. y=(4x-4)(2x+1) OA. 16x-2 B. 8x-4 OC. 16x-12 OD. 16x-4

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Q: 9y" + 30y' + 25y = 0, and y(3) = 9, y (3) = 3. %3D

A: For the complementary solution consider the quadratic  9m2+30m+25=0 The equation has repeated roots…

Q: Find y". y = x(3x + 1)* y" =L

A: Given function is  y= x(3x+1)4  We have to find : y".

Q: -3x у" + 5y' + 4y %3D 10е'

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Q: 3. (2x – y)3 = 3x?y, find y' %3D

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

A: See 2nd step

Q: Solve (3x*y? – x²)dy + (4x³y3 - 2xy)dx 0 %3D | | .3

A: Given differential equation is exact differential equation. We solve it as follows:

Q: Find y'' for y = 5x +4. 25x2 y'= - O A. 2 (5x? +4) 1 y" = O B. 4 (5x2 + 4) 20 y" = OC. (5x? + 4)…

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Q: Solve (2x – 1)3y" + (2x – 1)y' - 2y = 8x? – 2x + 3 %3D |

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Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…

Q: What is the solution of the y'''-(y'')3=0 You can find given options at the attachment. Thanks for…

A: Given y'''-(y")3 =0  The given 3rd order nonlinear ordinary differential equation.

Q: Find y". y = x(3x + 2)*

A:

Q: 2. y" + y' = cscx %3D

A: 2. we have  y''+y'=cscx  first find C.F m2+m=0m(m+1)=0m=0,-1y(x)=c1e0x+c2e-x=c1+c2e-x

Q: * If y" = 9x – 6x² ,y'(2) = 4, y(2) = 12 ,find y %3D

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Q: 4. (3x – y)2 = 6x + 2y + 23 @ (1,-2) 5. x(x² – y²) = 3 @ (-1,2)

A: 4) (3x-y)2=6x+2y+23, @(1,-2) 5)x(x2-y2)=3, @(-1,2).

Q: 9. (x? + 2ху — 4у?)dx - (x2 — 8ху — 4у?)dy %3D 0. |

A: We will use substitution y=tx  as shown below to evaluate this

Q: Find y'. 9) y = (5x-2)(3x + 1)

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Q: 1. Solve for 'x': vx + v2x +7 = 8

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Q: 1. y = x3 – 2x² + 3x – 5 - - dy 3x2 – 4x + 3 - dx

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0

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.