Find the solution of the given initial value problem. 6y" + 144y' – 960y = 0; y(0) = 12, y'(0) = 42, y"(0) = -360. y(t) = How does the solution behave as t → o? Choose one

Q: Find the solution. y'+=V5.y(1) = 0

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Q: Q2: Find General Solution (YGS)to the equation (Y4-1) Y=COS(2x)

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Q: Data stored on a computer disk or transmitted over a data network are usually represented as a…

A: Given that each byte is made up of 8 bits.

Q: Find the general solution of the following DE in explicit form. y' =2+2/y-2x+11

A: Solution: The differential equation is y'=2+2y-2x+11 Suppose that v=-2x+y so that y=v+2x Then,…

Q: 3. Solve y" + 2y + y = U(t-1) + 6(t-2), y(0) = 0, y'(0) = -1.

A: Some of the properties of Laplace transformation are ,…

Q: Q.4. Solve: y" – y' + y = Vxe*

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Q: y? + 3xy Solve the IVP y' y(1) = 5 using appropriate substitution. x2

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Q: Use the convolution to write a formula for problem: y" + 25y = f(t), y(0) = -2, y(0) = 1. |

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Q: p" +2y' – xy = 0 n(x)= e

A: Given

Q: (2.) Find the general solution to y' + 2ty = 5t.

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Q: Find a general solution of the equation: 3x?y" + 2xy' – 2y = 0

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Q: Eliminate the arbitrary constant. 2x y=c₁' e B A y"-y'- 2x=0 C -X (D) +c_e 2 y"-y'-2y=0 2y"-y'-2x =…

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Q: 3. Solve the DE: Y'=e2x+ 3y.

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Q: 2ty t²+1 – 2t – (2 – In(t² + 1))y'

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Q: Find the particular solution. y' = ex − 8;    y(0) = 9

A: Given, y' = ex − 8

Q: 1) y'+ = 5, y(1) = 4 Solve

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Q: Solve y′ = 2(10 - y), y(0) = 1

A: Given- y'=210-y and y0=1 To solve- The above differential equation.

Q: Eliminate the arbitrary constant. + c₂2e²x y=c₂₁e 1 A B C D -X y"'-y'-2x = 0 y"-y'-2y=0 2y"-y'-2x=0…

A: The given equation is: y=c1e-x+c2e2x...(1) To eliminate the constants c1 & c2.

Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: Find the general solution of the following equation valid near the origin: (1+4x2)y''-8y=0

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Q: ind the general solution x'y"-3x'y"+6xy-6y= 2x as assume x > 0

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Q: Solve 2y-y² sec²(xy²) + (2x−2xysec² (xy²)) y'= 0; y(1) = 2

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Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

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Q: Find the general solution of y" = 6y' – 9y where y is a function of x.

A: Given differential equation, y''=6y'-9y Find the general solution of the differential equation.

Q: Find solution y, of the equation y" +y' -6y = 0.

A:

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.