The general solution of 4y" + 4y' + y = 0 is y(x) = %3D (A) c1e-2¤ cos(x) + c2 e¯2ª sin(x) (B) c1 e2ª + c2x e2ª (C) c1e-2ª + C2 e2¤ (D) cje¯ + czxe¯}- + C2xe¯ (E) None

Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: The general solution of (D2-2D+1)y=2sin x A y= ce*+c>xe* + sinx B y=ce*+c2xe* + sinx+cos x…

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Q: (D² - 4D + 5)y = e*; y a. y= e²*(C,cos2x + C,sin2x) – –e 10 b. y e2*(C,cosx + C,sinx) +e 10 C. y =…

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Q: 2) If y = cos x, what is y (®(x)?

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Q: The solution of (e +2ay) daæ + (2 cos 2y+ 2x?y) dy is given by (A) e" + a?y² + cos 2y = c (B) e +…

A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

Q: The general solution of y" + y = e + 5e2* is y = ei (A cos (*) + B sin )) + Ce-" + 응e2x 2 () V5z y =…

A: Given that  y"'+y=e^(-x)+5e^(2x) To find the general solution

Q: The solution of (e+2xy?) dx + (2 cos 2y + 2x?y) dy is given by (A) e + x?y? + cos 2y = c (B) e +…

A: To find The solution of the given differential equation.

Q: The solution of (e + 2xy?) dx + (2 cos 2y + 2x y) dy is given by (A) e +x'y² + cos 2y = c (B) e"…

A: Given D.E is (ex + 2xy2) dx + (2cos 2y+2x2y) dy = 0     To find the solution of the given D.E .

Q: dx 4. -' (x- 3)*

A: Solution is given below

Q: 8 410x-32+x2 cos2x 4 Find *: (a) y =

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Q: Find the solution. (D4+2D³ + 10D²)y =0. y = c,+c,x+e¯*(c,cos3x +c,sin3x) C B y = (c,+c,)x+e-(c,cos3x…

A: Given Differential equation is D2+2D3+10D2y = 0

Q: Match the graphs with their parametric equations. I O (a) x=4-t+2, y = ² O (b)x= 2 - 3t, y = √t O…

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Q: Suppose that ye cos Bx is a solution of y-y +ay -9y =0 where a and B are real constants Then the…

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Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

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Q: A pyramid 3 m high has a square base that is 3 m on a side. The cross-section of the pyra- mid…

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Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

Q: The general solution of (D²+2D+1)(D²+4)y=0 is A y=(C,+C,x)e+C,cos2x + C ,sin2r B) none of the given…

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Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: z.e +4 a'z cos(2x+y) z.e Solve ax 4 əx-əy axəy

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Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: The general solution of y" + 4y' = 12 can %3D be written as (A) y = c1+ c2e¬2= + c3e2 + 3x (B) y=…

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Q: S z²+32 +4 24-72³ +11 2²-282 +28 dz?, GZ1 = 1

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Q: The solution of у" + у 3D 0, у(0) — 0, у'(0) — 1 is y(a) = (A) cos x (B) sin x (С) 1 — е ӕ (D) 1– eª…

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Q: The general solution of the equation (D*+D)y=-12 is y-+x+ccosx + c,ainx +6x ® y-c, + cx + cycosx +…

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Q: √x³+9y³ 5x +COS (+)

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Q: (1) y "'+ y "– 2y = 3+2cosx

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Q: y= (12,4 + x)* + (1+)(Va² +x- c )cos²(4x), c)cos²(Ax), 3)4( 3 y = (12,4 +x)* + (1+x' Зx +x — с y = ?

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Q: 2sin(y)cos(y) sint(y)+costy) dy

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Q: 3. [ (sec²(a) — csc²(a) + π) da

A: We will use formulas of integration to solve it

Q: (D4 + 18D2 + 81)y = 0 (A y = (c, + c,) cos3x + (c,+c,) sin3x. (B у %3 (с, + сх) cos:3x + (с,+c)…

A: To solve the given differential equation first we construct auxiliary equation and then solving the…

Q: In implicit differentation problems it seems we treat x and y differently. For example, when we…

A: Recall: Chain Rule of differentiation :    If F(x)=f(g(x)) then ,   F'(x) = df(g(x))dx =…

Q: COs ax dx. x² + b² (q)

A: Cauchy residue theorem: If f is holomorphic function defined on simply connected open set with…

Q: 4. Consider a3(x)y"" + a2(x)y" + a₁(x)y' = 0 (a) What's one trivial solution? (b) Suppose the…

A: Please see the attachment

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.