-2t A particular solution of the equation y" + y − 2y = 3te has the form O e 2t (At+B) + Ct cos(2t) + Dt sin(2t) −2t (At² + Bt) + Ct cos (2t) + Dt sin(2t) O e−2t (At² + Bt) + C cos(2t) + D sin(2t) + cos(2t

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" +…

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Q: Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" +…

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Q: b) 6(sin x)² + cos 2x + 1 = 0 [0,2π] I

A: Solution6 sin2x+cos 2x+1=0we know cos 2 x= 1-2 sin2xput this value in the given equation,6 sin2 x+…

Q: Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) +…

A: Given that  Equation : 2x sin2(y)dx - (x2+18) cos(y) dy = 0 and Implicit solution : ln(x2+18)…

Q: cos(2) is equal 1 اخترأحد الخيارات 2-2 sin(z) dy dx dz 2 – z 4-2 r/2 sin(2z) dy dx dz 4 - z z-2 cx/2…

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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: y" + 4y = 2 sin 3x + 3 cos 2x Find the solution y(x)

A: Given differential equation We have to find the solution of the differential equation.

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: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA…

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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: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: 1 Evaluate [ (x³ +cos(3x))dx 2

A: The given integral is ∫x3+12cos3xdx.

Q: If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry…

A: Given  z=x2+y2      and x= t cos 2r ,y= r sin t First substitute x,y values in z  Then derivative…

Q: Write down the form of a particular solution to the equation y" + 2y + 2y = 5e¯* sin(t) + 5t³…

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Q: 11. True or False: The general solution of -y = ) sin x is y-2 =(2x cos x - 2 sin x + c) 12. True or…

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Q: |(5e" + 5x4 =. + 9 cos x)dx 5et + x + 9 sin x + c 5ea + x + 9 cos x + c 5e + x³ – 9 sin x + c O et –…

A: Need to find integration

Q: The function y = 4e3x sin x is a solution of dy = 3y + 4e3x cos x dx A) True B) False

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Q: on of y" – 2y' + 2y =

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Q: Find dy dx 1) y = -1/323 ; tan 43 2 y = sec 5x 3) y = cos cos 2x + tan¹ \/ / 4) y = cot²¹ 2² 2 5) =…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: The equation ? + sin(xy) + C = 0 is the general solution of O y' + cos (xy) = 2 (x + y) 2 (ydx +…

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Q: ㅠ [sin(y) sin sin (y) sin² (y) 1+ cos(y) dy KIN

A: We will use substitution method to integrate.

Q: The solution to the IVP, is x₁ = 13x1 x2, x1(0) = x2 = 34x1+7x2, x2(0) = -1 x1(t) = e10t (cos(5t) +3…

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Q: Use the method of undetermined coefficients to find one solution of y" - 4y + 14y = 80e²t cos(3t) +…

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Q: | (6e"+6x° +4 cos x + 2)dx = %3D 6e + x° + 4 cos x + 2x + c O e – x° + cos x + 2 + c 6 O e + x° 4…

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Q: 2) y"+y' - 1 = 3 cos(x)

A: 2.

Q: y = 2 sin(2x) +11 30 30 30 Park 8. y = cos(36) 3- 1 537x 2 424 4 sin)-1 9. y 45 . 2 34 36

A: Note: Since Multiple Questions are asked, I am solving the first question, Kindly ask other…

Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

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Q: Solve the following 1 1) y dx + x² + y? dy = 0 x +y 2) (3x? In x+ x² –y) dx- xdy = 0, y(1) = 5 dy…

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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: Select the general solution to the equation. y" + 16y = 0 %3D Oy= C1 cos(-4x) + c2 sin(-4x) Oy= cie…

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Q: 2) x³y? = 2x + 2y3 3) y = sin?(x) – cos³(2x) + 2 www. .

A: