Find the general solution Solution 8. y= c, +c, cos 2x+c, sin 2x- 7 e* cos 2x+ 85 6. e* sin 2x 85 8. y"+4y = e* cos 2.x

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

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Q: What is the general solution of the differential equation y" +4y= tan 2x? Oy C1 cos 2x + C2 sin 2a -…

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Q: Find the general solution of the given Ordinary Differential Eqauations system: - 9 x () where X(t)…

A: .Our general solution is of the form X(t) = C1V1eλ1t + C2V2eλ2t  where V1 and V2 are eigenvectors…

Q: What is the particular solution of the function 3e" sin 5x – cos 5x? A cos 5æ + Bsin 5x + C'e" cos…

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Q: If x = sec e - cos e and y = sec" 8- cos"0 (x² + 4) (* - n°(y² + 4) = n²(v² + 4) Prove or disprove…

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Q: If y = cos x + sin 2x, find the value of y" - y + 3) O 2 cos x + sin x – 2 cos 2x – sin 2x O 2 cos x…

A: Given that: y=cosx+sin2x

Q: Use the method of undetermined coefficients to solve the initial value problem. 33 y ==cos2t 10 33…

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Q: y = In(cos 3x) %3D 1 (- sin 3x)(3) Cos 3x y' %3D y' = 1 (- sin 3x) cos 3x 1 y' = (3) sin 3x %3D -…

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Q: Write down all possible methods in which the (х- differential equation 2x = 2y) dx/dy can be solved.…

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: What substitution should be used to solve the integral x²dx 4-9x2 sinu=3x/2 O sec u =2x/3 O sec u…

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

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Q: I solved the separable equation and got 2/3y^3/2 = -2sqrt(x)cos(sqrt(x)) + 2sin(sqrt(x)) + C, but I…

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Q: Find the general solution to 2- ди u = xt + x cos t + t sin x. 3 - -

A: Given: 2∂u∂t-3∂u∂x-u=xt+x cos t+t sin x

Q: 24. Evaluate: S(cos 2x) esin 2x dx A. -e sinzx + C esinzx +C C. esinzx + C esinzx D. + C В.…

A: using substitution method to solve integration

Q: S cos(3z)sin1º(3z) dz C 1 (cos (3z))10 + C 3. (sin(3z))10 + C D 1 (cos (3z))1 + C 33 (sin(3z))'l + C…

A: Topic = Integration

Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

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Q: What is the particular solution of the function 2xe3 sin 7x – 8x?? O Aa? + Bx + C + Exe3, cos 7x +…

A: NOTE: Refresh your page if you can't see any equations. . . the second function is  which is a…

Q: Step by step

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Q: int (1,7), given that  y = 2x2 + 3x + C is a general solution to the differential equation. Hint…

A: The differential equation given is, dydx=4x+3. Integrate the differential equation,…

Q: 2. +4y= sin(3t), y(0)=2, y'(0) = 0

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Q: obtain in alinear differential eqaution with real, constant coefficients that is satisfied by the…

A: The solution of the problem is given in the next step.

Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

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Q: -) Solve the following partial differential equation us ing direct integration: a²u = cos (x +y) дх…

A: Topic:- application of integration

Q: What is the c value obtained for the special solution of the equation under the initial condition y…

A: Here we have to find constant of integration c.

Q: 4. y" + 4y = sin² 2x when y () = 0; y' ( = %3D

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Q: Use the method of undetermined coefficients to solve the initial value problem. O y y = y = y = 33…

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

A: Calculation shown in the solution is correct , i am providing you the  answer for each boxes…

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: Solve for the differential equations and get the general solution. Simplify your answer free from…

A: The given differential equation is dy=tanxtanydx

Q: Find and simplify the result whenever possible dx 1. y=x+sin2x 1. y = 4 1 sin' 5x 3 2. y sin5x - 3.…

A: Solving for the number 4:                                          4) y=3xcos(x3)-9 sin(x3)   To…

Q: S sin x coszxdx = cosix + c cosix + O Option 2 O Option 3 -cosix + e -cosix + c O Option 4 O Option…

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Q: z sin(2- 32)+cos(2 - 3a)+c | 4x cos(2 – 3x) dx 4x cos(3 3r) dx Option 1 Option 2 |4 cos(3- 3z) dr…

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Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0 %3D

A: Given, y = 7sin2x +9cos2x  We have to verify y = 7sin2x +9cos2x is a solution of y"+4y = 0

Q: Find the general solution 6. y"+4y' = sec2x Solution 6. y=c, +c, cos 2x+c, sin 2x+ 16 sin 2x -In(sec…

A: Given differential equation is y'''+4y'=sec2x We have to find the solution of the given differential…

Q: 35. Given that d = 6(sin 2x - cos 3x) and y = 0 dx when x = 0, y = A -3 cos 2x - 2 sin 3x – 3 B 3…

A: We can solve this problem using initial value problem.

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

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Q: Solve x4) +6x³y/3) + 25x²y +19xy` +81y=0 where x>0 O c, cos(3/nx) + c,sin(3/nx) + C3cos(3/nx)inx+…

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: Solve the initial value DE y - ytanz = sinx, y(o) = 1 5-Cos 2x 5-Cos 3x 5-Cos 2x Cos 2x A) y = B) y…

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

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Q: The general solution of y"+ 16y3cost is: Select one: а. y = C, cos(4t) + C, sin(4t) + tcost 15 b. y…

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Q: Solve the initial value problem y′′ + 9y = cos(3x)+sin(3x) for y(0)= 2, y′(0)= 1.

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Q: 6. Vsin x sin 2xdx Vtan 4x 7. J cos² 4x 8. cos 2xsin 2.xdx |arctan(3 – x) - dx 9. 1+ (3-х)? 3e 2y…

A: Given

Q: Is the differential equation y sin 4x dx + x cos 9y dy = 0 exact? %3D Choose the most appropriate…

A: A Diffrentaial equation in the form :-  M( x, y)dx + N(x, y) dy = 0 is an exact  if,   ∂M/∂y =…

Q: The general solution of y" + 16y = cost is: Select one: а. v = C,cos(4t) + C,sin(4t) + 1 -cost 15 b.…

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Q: Find the general solution of cos(x) y' +sin (x) y = 2 cos^3(x)sin (x)-1 And determine the method of…

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Q: azu Ex: Solve the partial differential equation дудх sin³x cos²y given that du %3D siny when x=0 and…

A: First take x as a constant and integrate with respect to y and the other one

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.