Obtain the general solution. (D² + 1)y= secx O y= C,cosx+ C2sinx + xsinx - cosxln|cosx| O y= C,cosx + C2sinx+ xsinx + cosxin|cosx| O y= C¿cosx+ C2sinx+ xcosx + sinxln|cosx| O y= Cịcosx + C2sinx + xsinx+ cosxIn|secx|

Q: Find the general solution of (D*+50D²+625) y =0̟ A y=c,cos5x + c,sin5x + c zxcos5x + c „rsin5x 5x Sx…

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

A: First I have find the complementary function and then particular solution, Adding these two gives…

Q: 3. Determine the general solution. a) y"–2y' – 3y= e* b) y"+9y= cos x

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Q: Find the general solution: x(x^3-xy^2+2y^3 )dy-y(x^3+2y^3 )dx=0 O A. xy^2 In [y+x^3-y^3=cxy^2 )] B.…

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Q: Find the general solution of (D4+ 50D²+625) y=0_ A y=c,cos5x +c,sin5x ® y=c,e*+c,x* +cze-5«.…

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Q: Find the general solution. (D³ - 14D +8)y = 0 a. y = c1e¬4X + cze(2+v2)x + c3e(2-vZ)x b. y = ce*x +…

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

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Q: Solve: (16 y – 24a? y4) dæ = (32x³ y³ – 20x*yA – 6 sin 2y) dy - O 7x* y% – 5æ°y – 3 cos 2y = C - O…

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Q: y(7) −4y(6) −4y(5) + 56y(4) −156y(3) + 224y'' −176y' + 64y = ex cos(x)−3e2x + xe−4x Which is the…

A: Given: y(7)-4y(6)-4y5+56y(4)-156y3+224y''-176y'+64y=excos(x)-3e2x+xe-4x ....(i) The Characteristics…

Q: Find the Particular Solution: y(x - 6y)dx - x(2x - 9y)dy = 0 ; when x=1, y=1 O a. y (2y-3x) = 3x? O…

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Q: (D3 – 6D2 + 4D – 24)y = 0 A. y = ce6x + Cze2x + Cze-2x B. y = ce6x + e*(c2 cos 2x + c3 sin 2x) C. y…

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Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: The general solution of xy" - xy' + (24x* – 24 y = 0, is .a - C,xY,(2 /6x) b O C,xJ,(2 6x) +…

A: We have to find the general solution of the differential equation…

Q: Solve (D2 – 2)y =0 O a. y = cqevZx + c2e¬vZx O b.y= "(c,cos/2x+ c,sin/2x) O c.y = cqevZx+czxe¬VZx O…

A: The equation D2-2y=0 represent y''-2y=0 . Consider the solution of the differential equation is in…

Q: Solve: y/" – 4y" + 53y = 0 O y = C1 + C2e cos2x + C3e-7* sin2x 7x O y = C1 + C2e cos2x + C3 e7"…

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Q: 11. Determine the general solution of y" + y = tanx using variation of parameters a. y = C₁xsinx +…

A: We have to use Variation of Parameters to solve the differential equation. y'' + y = tan  x

Q: 5. Find the particular solution of (x + y – 3)dx + (x +y + 5) dy = 0 when x = 1, y= 0. a. (x + y +…

A: Simplify the given equation. (x+y-3)dx+(x+y+5)dy=0⇒(x+y+5)dy=-(x+y-3)dx⇒dydx=-(x+y-3)(x+y+5)…

Q: Find general solutions 17. y" - 4y = -12x² + 6x-4; 18. y"+y+y = -13 sin(2x); 19. yy=e+ I; 20. y" -…

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Q: The general solution of (D3+4D)y 0 is y= e"(c,cos2x+c,sin2x) y=C+c2x+C3e ax B © y=c+c,cos2x+c3sin2x…

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Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

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Q: Solve: y" + 4y" + 29y' = 0 O y = C1 + C2e5ª cos2x + C3e5" sin2x -2а O y = C1 + C2e¬2ª cos5x + C3e¬2®…

A: The given equation is y'''+4y''+29y'=0 First write the auxiliary equation and then solve it to…

Q: 9. (y³+4)√1- cos² (y4 + 16y) ». f (y ³. cos(y¹+ 16y) () 2. dy

A: Answer of the above integration is

Q: Find the general solution (D2 + 9)y = 5e-162x a. y = C1 cos 3x + c2 sin 3x + 18x + b. y = c cos 3x+…

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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: 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: Find the function y(x) satisfying -8/9 = 6x dx and y(-1) = - 4. dy :-8/9 The function y(x)…

A: Integrate the equation dydx=6x-8/9 with respect to x.…

Q: The general solution of (D<-2D+1)y=2sin x y=cqe*+c2xe* +sinx В y=cqe*+c2xe*+cosx ©…

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Q: f(t) = e3t + cos(6t) – est cos(6t) As4 + Bs3 + Cs² + Ds + E F(s) Fs5 + Gs4 + Hs3 + Is² + Js + K

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Q: What is the general solution of (D° + 14D³ + 49D) y = 0 Oy = (C1 + C3z) cos v7a + (C2 + C4x) cos 7z…

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Q: Solve: (24x y- 15x y + 10 sin a cosa cosy) da + (40 y - 12 y-5 sin² a sin y) dy = 0 O 8a* y-3a y-5…

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Q: Find the general solution of (D4+ 50D2+ 625) y=0 (A y=c,cos5x + c,sin5x +czxcos5x + c „xsin5x B)…

A: Let's find.

Q: (D³ – 3D² + 9D + 13)y = 0 Find the solution. y = c,e- +c,e* cos 3x + c,ez" sin 3x y = c,e* + cze*…

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Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

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Q: 1. Find the general solution. а. (3х — 2у + 1) dx + (3x — 2у + 3) dy — 0 Ь. dy/dx 3D (9х + 4у + 1)?…

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Q: (D^2+1)y=10e^2x ; when x=0. y=0, y'=0. Ans: y=2(e^2x-cosx-2sinx)

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Q: The general solution for the DE 4y'+20y +25y=0s O e. None of these. 5x O d. y= c, sin()+ c,cos().…

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Q: Solve for the general solution of (D: - 1)y = sinx using variation of parameters y = cje¯* + ¢ze*…

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Q: dy - Find the general solution of Y +2 = 3x²y² dx A. 1/(xy) = -3(x³/2) + C B. 1/(xy) = -3(x²/2) + C…

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Q: This is the solution of y" + 4y' + 3y = 8 (t – 2) , y (0) = 0, y' (0) = 0 O y = [e-t-2) –e-8(t-2)] U…

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Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: What is the most appropriate substitution equation in order to solve the equation…

A: The given differential equation is -  (x+2y-1)dx+3(x+2y)dy=0 Rewriting the above equation as  -…

Q: What is the general solution of (D³ + 12D³ + 36D) y = 0 ? Oy = (C1 + C3x) cos 6x + (C2 + C4x) sin 6x…

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Q: - general solution for the Euler DE x²y• - 3xy +6y=D Cy=Cxcos(/2 Inx) + c2xsin(/ZInx). a y= Cx+…

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Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 11-20.

A: (10)Consider the provided function, fx,y=x2+2xy Find all the local maxima, local minima, and saddle…

Q: Consider the IVP: y" +9y = 40e*; y(0) = 5, y'(0) = -2. Find the general solution. (A) y(x) =…

A: The given differential equation is second order linear, homogeneous differential equations with…

Q: Let y" - 2y' +y = x²(cosx) + e5%. Then we can write a suitable form of a particular solution as: Yp…

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Q: The general solution of (D³+4D)y=0 is A y=ce*+c2ex+ C3e=2x B y=c+c2x+cze¬4x y=c1+C2x+C3e- B ©…

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Q: The general solution of y" + 4y' = 12 can be written as (A) y = c1+ c2e¬2 + C3e2" + 3x (B) y = c1 +…

A: We have to find the general solution of the given differential equation y'''+4y'=12 .

Q: Find the general solution of (D4+50D²+ 625) y=0 A y=c,cos5x+c „sin5x y=c,cos5x+c,sin5x + c zxcos5x+c…

A: Answer: option C is correct answer To find: general solution.

Q: Find the general solution to (D5-2D3-2D²-3D-2)y=0 O y= e-X(Cı + Czx) + C3e2X + C4COSx+ Cssinx…

A: Sol:- This can be written as :- D5-2D3-2D2-3D-2=0D+12D-2D2+1=0D+1=0  or   D-2=0  or   D2+1=0The…