Question 5 Find the general solution of the differential equation u" +25u = 7e". 7 u(t)=C, cos 5t + C, sin5t + 4t 41 41 -25t o u(t)=C, + C,e + 7 7 o u(t)=C, + C, e + -25t 41 41 o u(t) =C, cos 5t + C, sin5t + 7 A Moving to another question will save this response.

Q: 2. Find the general solution of the differential equation: dr = 2 cos(30) sin(30) op А. 6r - cos(6ө)…

A: I am going to solve the given problem by using some simple calculus to get the rwquired result.

Q: Given partial differential equation i u, +2tu, = -sin x %3D ii u+2(u„)´ +u, = cos x %3D Based on the…

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Q: one solution of the differential equation is given. Find the general solution. 6y 4 +5y3…

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Q: 2. Find the general solution of the differential equation: dr = 2 cos(30) sin(30) de А. бr - cos(60)…

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Q: The solution of the differential equation 5/1 – x2 ? dy dx 7/1 - y? = 0 is - 5 sin-x – 7 sin-y = C 5…

A: Question is solved.

Q: tan(6 ex) is a solution of the differential equation y' + y = 3T with the initial condition y( - In…

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Q: State the order of the given ordinary differential equation. (1-x)y" - 5xy' + 2y = cos x Determine…

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Q: State the order of the given ordinary differential equation. (1 x)y" 9xy' + 2y = cos x Determine…

A: state the order of the given differential eqation . and detemine whether the equation is linear

Q: If y1 = cos 3x and 2 = sin 3x are two solutions of a second linear differential equation. Then the…

A: B. 3

Q: A 30-V emf is connected in series to an inductance of 0.1 henry and a resistance of 50 Q. Initially,…

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Q: 4. Find the differential equation of the family circles entered at (h, k) passing through the origin…

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Q: The equation, sin y-2 sin(2) sin(2y) y+ cos z + 2acos () cos(2y) = 0 is an exact differential…

A: We have to solve

Q: Solve the differential equation. 13. ( sin θ – 2r cos^2 θ) dr + r cos θ ( 2r sin θ + 1) dθ = 0

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Q: Determine an appropriate choice for a particular solution for the differential equation y" + 4y = 3…

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Q: II. Solve the given linear differential equation showing the details of your work. 1. (D²…

A: The given differential equations are;  1) (D2-3D+4)y=16x-50Cos2x 2)(D2-3D+2)y=Sin(e-x).

Q: Solve the differential equation [cos (2y) — 3x²y²] dx + [cos (2y) - 2x sin (2y) - 2x³y] dy - a. sin…

A: Given: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0

Q: 3.(ii) Show that given differential equation is not exact and hence solve it. |(2y – 4xy")dr - (2³ –…

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Q: Which one is false? If the auxiliary equation of the homogeneous linear differential equation has…

A: Let us check which of the information given is false in the next step.

Q: State the order of the given ordinary differential equation. (sin 0)y"' – (cos 0)y' = 8 %3D…

A: NOTE: Refresh your page if you can't see any equations. . The order of the highest derivative term…

Q: Solve the differential equation. 10. ( cos 2y – 3x^2y^2) dx + (cos 2y – 2x sin 2y – 2x^3y) dy = 0

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Q: Let y %3D x-3 (a) Find the general solution to the given differential equation; (b) Find a…

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Q: Do the functions y = cos5t and y, = sin5t constitute a fundamental set of solutions of the…

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Q: From the equations in the picture, a second-order differential equation for UC can be made on the…

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Q: Find the solution of these differential equations : 1. dx %3D

A: Given Since You have posted multiple questions, so we solve the first question for you, to get the…

Q: x+ y, (e* + In y)dx + (dy = 0

A: We have to solve the given first-order differential equation…

Q: 10. (a) Show that the differential equation (4x + 3y?) dx + 2xy dy = 0 is not exact. (b) Find an…

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Q: State the order of the given ordinary differential equation. (1 - x)y" - 9xy' + 5y = cos x Determine…

A: The given ordinary differential equation is…

Q: Problem 4 By finding the second order differential equation solved by x, find the general solution…

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Q: State the order of the given ordinary differential equation. (1 – x)y" – 3xy' + 4y = cos x %3D…

A: NOTE: Refresh your page if you can't see any equations. . the Order of a differential equation is…

Q: Consider the differential equation y" - 2y + 17y= 0; ex cos(4x), ex sin(4x), (-∞o, co). Verify that…

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Q: Do the functions y₁ = cos5t and y2 = sin5t constitute a fundamental set of solutions of the…

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Q: 3 ± 5i If the roots of the auxiliary equation of a higher-order homogeneous differential equation…

A: To find y, if the roots of the auxiliary equation of a higher‐order homogeneous differential…

Q: If the auxiliary equation of a differential equation of order 2 has roots r1 =7 and r2 = 7, then the…

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Q: EXAMPLE 3: Solve the differential equation y" + y' = 3sin(2.x)+cos(2.x).

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Q: Determine the solution of the differential equation + 12 + 8 = 0 ds ds ds ds x = C, + C2s + Czež +…

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Q: Question 4 Determine the solution of the differential equation 7+12 ds ds + 8 ds = 0 a. x= C, + C2s…

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Q: 4. Find a second-order lincar equation for which y(x) = ce* + cze*z + sin(2r) is the general…

A: The homogenous part of the linear equation is, c1e3x+c2e5x. The particular part of the linear…

Q: Question 8 Find a homogeneous Euler-Cauchy differential equation whose general solution is Cx + C2x…

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Q: State the order of the given ordinary differential equation. 4 dy + y = 0 - dx 3 dx Determine…

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Q: Question 4 Solve the separable differential equation dy = 0.8y dz and find the particular solution…

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Q: To find the differential equation of y= c,e 2x c e“ cos 3x + c,e“ sin 3x, we use elimination of…

A: First simplify first derivative equation and then derivative it again with respect to x

Q: Select the general form of a particular solution for the differential equation y" + 4y =5 cos(2a). O…

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Q: 13) The linear differential equation whose general solution is given by x = Aet + Btet + cos(3t)…

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Q: Question 3: Solve the differential equation dr+y-e-* cos x = 0,0 sxs 0.5, y(0) = 0 by a) Milne's…

A: We are given the differential equation:dydx+y-e-xcosx=0 ⇒dy+y dx-e-xcosx dx=0⇒dy=e-xcosx…

Q: +8 dx = 0 Determine the solution of the differential equation d5x 2 dss d'x d³x d?x +12 +8 %3D ds3…

A: Given differential equation is 5th order differential equation. Since this is homogenous equation we…

Q: In the equation (ax+by+c)dx + (ex+fy+g)dx = 0, if b=e, then the equation is said to be exact…

A: A differential equation of the form Mdx+Ndy=0 is said to be exact differential equation if it…

Q: State the order of the given ordinary differential equation. d²u du + +u = cos(r + u) dr² dr…

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Q: Question 10 Let u(x,t) be the solution of the partial differential equation u, =Ux 00 with the…

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Q: 3. Solve the differential equation (1 + cos ). sin r +2 3y dy = 0 by using an integrating factor in…

A: The given differential equation is of the form, Mdx+Ndy=0 Where, M= 1+yx2cosxand N= x3y+2sinxx2

Q: 3. Show that the differential equation (cos z + 2y) dy + (r³ – y sin z) dr = 0 is an exact equation…

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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.