A. Obtain the differential equation of the gi- (1) 3x² – xy² = c (2) y = a cos(x +B) (3) y = c,e¬2x + Cze2x (4) y = x² + c,e2* + c2e¬* (5) y = c,e²x cos 3x + cze²x sin 3x

Q: The complementary function(C.F.) of the differential equation(D – 8)°y = sin 8x is (ci + c2x +…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: Find the general solution to the following Cauchy-Euler differential equation x2y" +27xy'+ 169y = 0.…

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Q: Determine the solution of the differential equation 2y(4) + 3y" + 2y" + 6y' – 4y = 0 %3D y = C,e2x +…

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Q: Solve the differential equation y" – 8y' + 17y = 0 A) y (x) = c, e** cos(x) + c, e** sin(x) B) y (x)…

A: It is given that the differential equation y''-8y+17y=0. This is a homogenous differential equation.…

Q: Form the differential equations from the following equations: 1. y ax + bx2, 3. xy Ae+ Be+x2. 5. y=…

A: The solution for the asked part  is given as

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Q: Find the differential equation of the following function (x + y – 1)dx + (2x + 2y + 1)dy = 0 a. x +…

A: We have to solve the differential equation

Q: Which of the following is the general solution of the differential equation y (iv) +21y"-100y=0? O…

A: We will find out the required solution.

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 of the differential equation (D² – 7D + 12)y= x² cos 3x is O CF = Ae 4x +…

A: first equate D^2-7D+12=0

Q: The complementary function(C.F.) of the differential equation (D² + 6D+18)y=x is_ -37 (c1 cos 3x +…

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Q: Solve the differential equation y"-3y'-4y 0 O y= e3* (c cos 2x + C2 sin 2x) cos 3x + c2 sin 3x) O y=…

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Q: Solve the differential equation x²y"+ 4xy'+ 2y = 0 %3D اخترأحد الخيارات y(x) = C1a-1+ C2x O %3D y(x)…

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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: 17. Determine the differential equation whose general solution is y = C,Sin3t + C,Cos3t . d? y - 9y…

A: Topic = Differential equation

Q: a. (y2-xy)dx + (x2-xy)dy = 0

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Q: Which of the following differential equation is non linear, second degree, dependent variable is y,…

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Q: Determine the solution of the differential equation y" - 2y' + y = 14 y = C,e + C,xe" +e* In(1 + x)…

A: First we find complimentary function then find particular integral then solution.

Q: Given the differential equation y" + 7y' + 12y = 8x e-3x Determine the General Particular Solution…

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Q: The general solution of the differential equation y" – 6y' +9y = 0 is | OA.y = e* (C1 cos 3x +c2 sin…

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Q: The general solution of the differential equation x²y" - 2y = Inx is O c,x? + c2xl + 2 lnx - 1…

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Q: Which of the following differential equation is non linear, first degree, and the independent…

A: We need to choose correct option.

Q: (a) Solve the Cauchy-Euler equation solution of the differential equation r²y" + xy + 4y = 0, r> 0.…

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Q: If r1 and r2 are the roots of the characteristic equation of the differential equation y′′−y′−6y=0,…

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Q: 15. Determine the differential equation whose general solution is x= C,e" + C,te® . d²x dx – 36+12x…

A: We need to determine the ODE for which the solution is given in the question. This can be done as…

Q: The auxiliary equation of a non-homogeneous differential equation has complex and distinct roots.…

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Q: The complementary function(C.F.) of the differential equation (D – 6) (D² + 6²)y = e&" is_ cie0a +…

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Q: The solution of the differential equation d²y +9y = cos 3t is y(t)= A sin Bt + (2C )tsin Dt Then…

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Q: Solve the following differential equations: 1. (r - y2) dx = 2xy dy 2. (x²y – 2xy?) dx - (r³ – 3x3y)…

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Q: 1. Determine whether the equation below satisfy its corresponding differential equation: y = C,e2x +…

A: The given differential equation is     y'''-2y''+9y'-18y=216 and we have to check whether…

Q: Determine if the differential equation y'=x4y - 9x5y is separable, and if so, separate it. dy Yes,…

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Q: Determine the solution of the differential equation 2y"-3y'+ 4y = 0 %3D 3X V23 V23 y = e (C, cos x+…

A: Let's find.

Q: Consider the differential equation: 1 1+e¯* What is the general solution? y" – 3y' + 2y = : Oy = [c…

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Q: The complementary function(C.F.) of the differential equation(D - 3)°y= cos 3x is O (cı + czx +…

A: Thanks for the question :)And your upvote will be really appreciable ;) As per guideline, only one…

Q: (9) The differential equation M(x, y)dx + (2ye* + y²e³x) dy = = is exact if (a) M(x, y) = e2x y² +…

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Q: Transform the differential equation xy" - 2y' + Axy = 0, into a Sturm-Linville differential equation…

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Q: Transform the equation y' differential equation. O (1 + x²) dx - dy = 0 O (1 + x²) dx 2x 0₁dx 1 + x²…

A: y'=2xy1+x2

Q: Which of the following equations can be reduced to the homogenuous linear differential equation with…

A: Differential equations are given, we have to find homogeneous linear differential equation with…

Q: Exercises: Solve the following exact differential equations: 1.(2+ye") dx+(xe"-2y) dy=0…

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Q: Solve the differential equation dy dx 9xy - 2y² 6x² xy O a. 3y³ O b. 3x³ x²y = 2y² x²y = 2y² O c.…

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Q: The complementary function(C.F.) of the differential equation(D – 3)°y=sin 3x is O (ci + c2z +…

A: Solution: The objective is to find the complementary solution of the given differential equation

Q: 10. Find the solution of the differential equation (D° + 8D° + 16D)y = 0 A. Y = C, + (C2 + C3x)cos c…

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Q: The complementary function(C.F.) of the differential equation (D – 2)°y = sin 2æ is O (c1 + Ca +…

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Q: 8. Find the solution of the differential equation (D* - 2D° + D*)y = 0 y = C, + C2x + e*(C, + y = C+…

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Q: Determine the solution of the differential equation 2y(4) + 3y"" + 2y" + 6y'- 4y = 0 y = C,ex + Czei…

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Q: (1) (a) Find the order, Degree and linear or Non-Linear Differential Equations for = va + 5/ỹ. d²y…

A: Answer

Q: 3 Find the solution of the differential equation (D° + 8D° + 16D)y = 0 y = C, + (C2 + C3x)cos C +…

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Q: How are the constants a, b, and c related if the following differential form is exact? (ay2 + 2czx)…

A: To Determine: how are the constants a,b and c related if the following differential form is exact?…

Q: The complementary function(C.F.) of the differential equation(D – 6)²(D+5)y= 6x is_ O (c1 + c2x)eôz…

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