- Solve the given differential equations using methods stipulated in the topics covered. Solve completely and Include all the details necessary to solve the problem. - 24) dy = o 2X + dx + 2 2. 2 2. when x = 4 * , y- 3

Q: (14) dx + xydy

A: Given

Q: Attached below is a description and the differential equations problem/question: Make sure to…

A: Undetermined coefficients.

Q: dy + (3х — 7)у 3 5x7 | dx

A: Consider the provided D.E,

Q: dy Q3. Solve the DE da +y - y? provided that y1 = - is one known solution of the equation.

A:

Q: 1) 2+37-4-0 2) 頭+32+2y-0 dx

A:

Q: a) dy dx xe ex²+ y(0)=1

A:

Q: Form the differential equation by eliminating A and B from Ax² +By² = 1.

A:

Q: Q1. Solve the following dy (a). y² + xy³ + (5y² – xy+ y³ sin y) = 0. dx

A:

Q: Problem 3 (Exercise 2.6.70) x" – 6x' + 5x= e5t +t?e-5t

A: Given that x''-6x'+5x=e5t+t2e-5t To write the actual particular solution form:

Q: 1. State the order of the following differential equations. Which are linear and nonlinear? dy а. dx…

A: 1,a) The order of the differential equation is 1, it is linear. b) The order of the differential…

Q: just find the correct solution form for the particular solution to the differential equation if the…

A:

Q: 2. Solve D²y + 3Dy - 10y = -130 cos(x) + 16e³x

A:

Q: (In x - 9Jax-(8 + 1) dy == 0 2. + 6x) dx + (Inx-2) dy = 0 3. (2x y2 + 24) dx + (2x²y + 2x) dy = 0 4.…

A:

Q: 3. Solve the Differential Equation: 2y (4) + 11y" + 18y" + 4y - 8y = x² - 5 Show your solution on…

A: Given equation 2yiv+11y'''+18y''+4y'-8=x2-5 Finding the C.F…

Q: 4x²yy' 3x(3y2 + 2) + 2(3y +2)3 %3D

A: Given differential equation is 4x2yy'=3x(3y2+2)+2(3y2+2)3 where y'=dydx We have to find the solution…

Q: 1. 7ху' — 2у + (E) - = 0

A: Given differential equation  7xy'-2y+xy6=0

Q: -3x (p²+p² - 5172+3) y = e +4e²

A:

Q: 3. Verify if y=2x-3 is a solution to y'-y-3 = -2x+5.

A:

Q: 12. Solve: a. y" + 6y' +10y = 0 b. y" - by' +9y = 0 c. y" - 5y' + 6y = 0

A: (1) Assuming  as trial solution.(2) finding the derivatives upto the same as order of the…

Q: You are given the differential equation 6y" – 6y' – 5y = 0. a) Form and solve the auxiliary equation…

A: The auxiliary equation is a quadratic equation.find the roots of the quadratic equation.

Q: 6. Use an analogy with differential equations to solve the IVP xo = 1, x₁ = 2 for the difference…

A: We will solve this by characteristics method, and after that we will use initial conditions to…

Q: -2t (1+t)y +4ty = 16e

A:

Q: x" + 25x = cos 5t

A: Given differential equation is : x''+25x=cos5t.     .....1 Homogenous differential equation will be,…

Q: Methods. Obtain the general solutions for each of the following differential equations. Each method…

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Q: 2. Solve the following differential equations using variation of parameters: (i) y" + 4y = 4 tan 2x,…

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Q: 43. (3x² + 4xy)dx + (2x² + 2y)dy = 0 Classify differential equations and show whether they are…

A: We will find out the required solution.

Q: 9 y" – y + ម = ( a + 3)e-x

A:

Q: Show that y = √√C-2x² is a solution of the differential equation particular solution that passes…

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Q: (Ax²y + 2y²)dx + (x³ + 4xy)dy = 0 i) If it is exact differential equation find the coefficient A. i)…

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Q: For the differential equations below, write in standard form, and name the type of equation. Then…

A: Here we will estimate the required form.