The complementary function(C.F.) of the differential equation (D – 7)(D² + 7?)y = e7² is O (c2 Cos 7x + c3 sin 7x) -7x O cie + (c2 cos 7x + C3 sin 7x) cjez + (c2 cos 7x+ c3 sin 7x) cielz + (c2 cos 7x – c3 sin 7x)

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: ven the differential equation (D3 + 9D² + 27D + 27) y = In(2x –- 3). Propose an appropriate…

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Q: The complementary function(C.F.) of the differential equation(D – 7)²(D+3)y = 7x is_ O (c1 + C2x)e=…

A: Differential equation and complementary function

Q: 1 Laplace transforms Calculate the Laplace transforms of (i) H₂(t) cosh (3t), where cosh (at) = 1/²…

A: Solution: (i) let, f(t) = H2(t)cosh(3t)                   = H2(t)[(1/2)(e3t + e-3t)]…

Q: d [cos³ (x²)-csc(x²)] dx

A: We are required to find the value of ddxcos3x2-cscx2     The following formulas of derivatives has…

Q: A third-order differential equation has a general solution of: y=e-2x(C₁ + C₂cos8x + C2sin8x).…

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Q: Find the general solution of the linear differential equations. (D +4D'y =12 x2 a. y = C, + C2x +…

A: Solved below

Q: The complementary function(C.F.) of the differential equation(D - 5)y= cos 5æ is_ O (ci + c2a –…

A: Given that  (D-5)^3y=cos5x  To find the complementary function

Q: The complementary function(C.F.) of the differential equation (D³ – 8)y = sin 4x is cje2" + e¯ c2…

A: We will solve the problem.

Q: Find the general solution of the linear differential equations. (D° +4D' þy =12 a. y = C, + C2x +…

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Q: Solve S(cosa{x – +)<(1 + +) dx -

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Q: Consider the second-order differential equation:  (d2x/dt2) + x (dx/dt) = sin x.  which option…

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Q: Write the smallest differential operator that annihilates the given 3x +x²e + sin(5x) e3 sin…

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Q: me complementary function(C.F.) of the di O (c1 + c2x + czæ²)e4z P (c1 + c2¤ – czæ²)et= - O (c1 +…

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Q: S cos(7x + 5) dx = (sin(7x+5))/7 + c* O False O true

A: We have to evaluate   ∫ cos(7x + 5) dx

Q: When the constant" c" is eliminated in the relation 2y² + 2xy = cx², Which of the following is the…

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Q: sinr where 0sI<R 3. a) Evaluate LF())where F()-o where t2 dy de 3x-3y+4 and dt = 2x-2y-1 dt b) Solve…

A: see below the calculation and explanation

Q: What is the solution of the differential equation 20분 +3분+2분 +6-4y=0? Oy=C₁e¹2 + C₂e²+ C3 cos √r –…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT yyy Ü♥¯ ¶ ☆ @ ! ! ?? !! ? ?! ¿ ¡ !? S❀ W X Х Х Х Х A * ✓✓✓ DO -…

A: We have not any digital tool .

Q: Which one of the following is a separable first-order differential equation? A 1² dx = 1²x² = 71³x²…

A: The given differential equations, A) t2dxdt-t2x2=7t3x2-18t7x2+7x B) xtdxdt-t2x2=7t3x2-18t4x2+7x C)…

Q: solve for y, In - y| +C = (1n|cos(x) – 1| +c)

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Q: The complementary function(C.F.) of the differential equation(D – 7) (D+4)y= 7x is_ O (ci + c2x)e +…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the general solution of the linear differential equations. (D³ - D² +D-1]y= 4sin x a. y = C,e*…

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Q: The complementary function(C.F.) of the differential equation (D – 7)²(D + 5)y = 7x is O (c1 +…

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Q: (4(x2-1) dx x²(x+2)

A: We will use partial fraction here

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.