1.3 number 13 verify that each given function is a solution of the differential equations

Q: y – 18y"'+ 81y'= 0

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Q: Guess the form of the particular solution (a) y" - 3y + 2y = et (b) y" - 3y + 2y = t²e²t 1

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Q: Question 3 Use Laplace transform technique to solve the initial value problem y + 4y = g(t), y(0) =…

A: First write the unit step function for the given piecewise function gt.

Q: Is y c + 2 xe Colution to y" + 2y' +y=0. A Verify y= 4 cos (2x) + 6sin (2x) is a solotion to y "44y

A: We will find actual derivatives and checking by substituting in differential equation that, if it is…

Q: sin x sin y dx + cos x cos y dy = 0 2 mydx — пхdy

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Q: (a) Find the unique quadratic polynomial y = ax²+bx+c that passes through the three points (1, 1),…

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Q: 14. y - 2ty = 1; y = e? e-² ds +e %3D

A: We have the differential equation given by y'-2ty=1. Now we need to verify whether…

Q: dy (b). 3x+2y y(-1) = –1. , dx 3x+2y+2 '

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Q: 2. y = ln sin(x - A) +B; y" +(y)² +1=0

A: Introduction: A function y=f(x) that satisfies the differential equation when f and its derivatives…

Q: 1. Find at least six non-zero terms of the power series expansion about x, 0 for a general solution…

A: Given : Differential Equation x2-x+1y''-y'-y=0To find : atleast six non-zero terms of the power…

Q: (x²+y)dx + dy 0

A: This linear differential equation

Q: Verlfy that y 9e** + 3e is a rolution OF y"- 18 y' t yso.

A: ***As per our guidelines, we are supposed to answer only one question at a time. Since you have…

Q: 9. (x + x* + 2x²y² + y4)dx +y dy = 0; when x = 1,y = 1

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Q: Solve the first order differential equation by separating variables.

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Q: y!V – y"'+ 2y' = 0

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Q: Let A be a 3×3 matrix, and let u₁ and u₂ be the first two columns of A. Assume that u₁ and u₂ are…

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Q: (xy + y ln y)dx + (xy + x In x)dy = 0; when x = 1, y = 1

A: 7. The given differential equation is  (xy + y ln(y))  dx + (xy + x ln(x )) dy= 0   ....(1) with…

Q: 6. (y cos x + 2xev)dx + (sin x + x²e° + 2)dy = 0; when x = 0, y = 0

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Q: Use Euler's method with step size h = 0.1 to approxi- mate y(1.2), where y(x) is a solution of the…

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Q: (x*y- xy")(xdy + ydx) + dy = 2xdx

A: To solve the differential equation we use some special form

Q: 2x [3x+y-yexp(-x²)]dx+[x² + 3y² +exp(-x²)]dy=0

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Q: x Iny dx + (x- In y)dy = 0

A: Use  term 'y ln (y)' instead  of 'x ln(y)' then we get the solution to DE.

Q: Day 0 1 People left in hotel (put initial value here - in this case, 100) 48 29 15 23456 852

A: The given table is  day People left in hotel 0 100 1 48 2 29 3 15…

Q: Use Laplace transform technique to solve the initial value problem y" – 4y = e*, y(0) = 0, y(0) = 0.

A: Given equation is y''−4y=e3t.....1 and y0=0, y'0=0. We know that Ly''=sYs−sy0−y'0 and Ly=Ys Take 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.