Find the general solution of the differential equation, cos rdy- (2ysinz 3) dz = 0/ A. yoos z-2 sin z +C-0 C. y cos r+2 sin z +C=0 B. ysin'z- 3 cos z+ C 0 D. ycos'r 3sin z +C 0

Q: Consider the differential equation given as y" – 6y/ + 9y = t-3,3t y (1) = e and y (1) = 0 Which…

A: Given: y''-6y'+9y=t-3e3t Auxiliary equation is m2-6m+9=0m2-3m-3m+9=0m(m-3)-3(m-3)=0m-3m-3=0⇒m=3,3…

Q: Find the particular solutions of the given differential equation dy dz 2 cos a sin a given y = 1…

A: 1. Sin(2A)=2sin(A)cos(A). 2. Sin²A+Cos²A=1.

Q: What is the general solution of the differential equation y" + 4y = cot 2x? Oy=G coe 2 +Gn 2-ain 2e…

A: variation of parameters, suppose it is desired to find a particular solution of the equation y″ +…

Q: Find the function y = y(x) (for æ > 0) which satisfies the separable differential equation 9 + 13z…

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Q: Find the particular solution of the differential equation (10x + 6x siny)dx + /x? +1(1+6ysiny+10y)dy…

A: Given differential equation: with x=0, y=0. Used formulas:

Q: Find the Wronskian of two solutions of the differential equation ty" -t(t-3)y' + (t5)y=0 without…

A: Given differential equation is t2y'' - t(t-3)y' + (t-5)y = 0

Q: Given the differential equation 2 y" + 18y = 6 tan(3x) Determine the value of u2. AH2 "3 =" 9*…

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Q: Verify that the given function y is a solution of the differential equation that follows it. Assume…

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Q: Find the value of k so that the differential equation (6ry³ + cos y) dr + (2kz²y² – 1 sin y) dy = 0…

A: we have to find the value of k when the given equation is exact            (6xy3 +cosy)dx…

Q: Find the values of the constant r so that y = e™* satisfies the differential equation 2y" + y' — у…

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Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t-3)y' + (t− 2)y =0…

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Q: Soru l: xe (0,+0) aralığında tanımlı d'y d. +1 diferansiyel denkleminin +6- -9y dx

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Q: Obtain the general solution of the given differential equation up to the form free from In function.…

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Q: Let y,(t) be a particular solution to the following second-order differential equation obtained from…

A: See the detailed solution below.

Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t− 3)y' + (t− 2)y=0…

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Q: Find a suitable form for particular solution of the differential equation y" + 2y' + 10y = te '…

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Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

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Q: Find the particular solution to the differential equation dy/dt = e^(t+y) that passes through (1,0),…

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Q: sinh(3x) +1 y = 3 6 sinh(3x) – 1 y = 6 2 sinh(3x) – 1 y = O y = sinh(3x) O y = sinh(3x)+1

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Q: Show that an implicit solution of 2x sin2(y) dx – (x² + 11) cos(y) dy = 0 is given by In(x + 11) +…

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Q: Give the general solution of the differential equation p"+ 25 y =2 sec( 5 x) a) O y=C, sin(5 x) + C,…

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

Q: 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0

A: First I have made the differential equation into variable seperable form and then solved them.

Q: Find the general solution of the second order differential equation dy dy 10 +24y 0 dar dr?

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Q: #3: Other than perhaps y y' = 2y* cos(7x)? 0, which of the following is the general solution to the…

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Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 17) cos(y) dy = 0 is given by In(x2 + 17) +…

A: To find- Show that an implicit solution of 2x sin2y dx - x2 + 17 cosy dy = 0 is given by lnx2 + 17 +…

Q: Verify that the indicated expression is an implicit solution of the given differential equation. 1 (…

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Q: : Consider the differential equation y" – 2y – 3y = 5 cos(2x). a) Verify that the family of…

A: This question can be solved by using the concept of solution of second order non homogeneous…

Q: 4. Solve for the general solution of the differential equation using homogenous equatiorn [x cos?…

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Q: Find the particular aolution of the differential equation with the initial condition given below.…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relatio y…

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Q: Let y,(t) be a particular solution to the following second-order differential equation obtained from…

A: y''-2y'+y=ett find the roots for a homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real root,…

Q: Show that an implicit solution of 2x sin (y) dx – (x² + 11) cos(y) dy = 0 is given by In(x2 + 11) +…

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Q: Find the general solution of the differential equation y" + zy' + 25y = 6 cos(5 In z) + 6 sin(5 In…

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Q: The general solution to an inhomogeneous second order differential equation is: y = Aer + Bent +ae*…

A: Given problem:- The general solution to an inhomogeneous second order differential equation is:   y…

Q: Find the solution to the differential equation that satisfies the stated condition. sin (5x + T),…

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Q: For x € 0,, What is the particular solution of the differential equation (y + ysinx)y' = /cos?x –…

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Q: use the fact that 5x^2 - y^2 = c is a one parameter family of solutions of the differential equation…

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Q: To solve the ordinary differential equation dy 3Y +5y2 = sinx, y(0) = 5 dx by Euler's method, you…

A: To solve the any ordinary differential equation by Euler method convert the equation in the form…

Q: Let y,(t) be a particular solution to the following second-order differential equation obtained from…

A: The complete solution of the equation is the combination of general solution and particular solution…

Q: The differential equation dy 4e" cos(y) + 3 dr 4e* sin(y) – 6y In(x) + 3y? Has solutions of form…

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Q: A second-order non-homogeneous differential equation is given by d2y/dx2 − 10 dy/dx + 21? = 21x2 +…

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Q: (x² + 4xy + 2y²)dy + xydx = 0

A: The solution is given as

Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: Given:     y''-6y'+25y=0     y=e3xcos4x      y'=ddxe3xcos4x  Apply the product rule:…

Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t− 2)y' + (t−6)y = 0…

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Q: Given: (6x - 3y + 2)dx - (2x - y - 1)dy = 0. Find the general solution of this differential equation…

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Q: Let y=g(x) be the solution to the differential equation dydx=xy−2 with the initial condition…

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: We have to solve given problem:

Q: To find a particular solution for the differential equation y"+4y = tan r with the variation of…

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Q: Find a suitable form for particular solution of the differential equation y" - 2y +2y = te' cos(t) -…

A: First option is true by choosing suitable constant

Q: To solve the ordinary differential equation dy 4 + 5y² = sin x ,y(0) = 5 dx by Euler's Method, you…

A: The given differential equation is       4 dydx+5 y2=sinx,  y0=5.......(i) We have to arrange the…