Which of the following is the general solution of the differential equation dy - sin? (2y – x)? dx a. In|cosec(x – y) – cot(x – y)| = -x+c b.-In|sec(x – y) + tan(x – y)| = -x+c c. In|sec (2y – x) + tan(2y – x)| = -x+c d.In/cosec(2y –x)– cot(2y – x)| = -x +c e.-In|sec(4y – 2x)+ tan(4y – 2x)| =-x +c 2

Q: A differential equation is an equation involving an unknown function and its derivatives. Consider…

A: In the question it is asked to calculate (i) The solution for the differential equation…

Q: Consider the first-order differential equation for y(x): dy = y tan x + sin x . dx du find a…

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Q: Given y(x) = c₁e²x + c₂e* + 2 sinx, find the values for ₁ and ₂ so that the conditions y(0) = 0 and…

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Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: 10. Find the 87th derivative of y = cos(2x) at IT

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Q: The solution of the differential equation 5/1 – x2 ? dy dx 7/1 - y? = 0 is - 5 sin-x – 7 sin-y = C 5…

A: Question is solved.

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

A:

Q: Save Determine whether the given function is a solution to the given differential equation. de…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: Show that there is exactly one solution f E L'([0, 1]) of the equation f(x) = 7 + sin(x) %3D

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Q: Solve the differential equation. dy y + 1 dx O In |x| – ? () = tan - ex - x + tan-'(x) = C In |x| –…

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Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: sin(x)=−0.2cos(y)=0.4tan(z)=5.5 sin(−x)= 0.2cos(−y)= 0.4tan(−z)= -5.5 What does…

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Q: (a)Deduce the 1$, 20d and 3rd derivatives of y = cos²x.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve: (cos x) · (dy/dx) + y sin x = 2x cos2 x, y(Tt/4) = (-15/2-n2)/32.

A: The given differential equation can be written as :            dydx +ytanx = 2xcosx So, the…

Q: sec y Obtain the solution of the differential equation y' x-4x+5 a. 2 sin y = In(x² – 4x + 5) + C b.…

A: ∫cosx=sinx +c∫dx1+x2=tan-1(x)+cCosx=1secx Given D.E y'=sec(y)/x^2-4x+5

Q: Show that w(t) =〈sin(3t + 4),sin(3t − 2)〉, cos 3t satisfies the differential equation w''(t) =…

A: Given- wt=<sin3t+4,sin3t-2>,cos3t To prove- That the above expression satisfies the…

Q: di miş Find the derivative a. O b. O C. O d. y' = y' = y' = y' = = dy of the function y = tan…

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Q: consider the differential equation dy/dx=sin(x)/y for which the solution is y=f(x). Let f(0) = 1…

A: Given dydx=sinxy, y0=1. By variables separation,  y dy=sinx dx Integrating on both sides,

Q: Find

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Q: d cos 2x – x³ i. dx 3 + tanh x

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Q: For an exact equation, Show that this differential equation cos(x+ y)dx= (3y² +2y+ cos(x+ y))cdy = 0…

A: We  are given the differential equation : cos (x+y)dx+(3y2+2y+cos(x+y))dy=0 On comparing with :…

Q: 19. The solution of the differential equation cos (2) dx - sin (²) + COS (²)]dy = 0 is A. y sec ² =…

A: Only one question is solved. Solving more than one question is solved in the policy of bartleby.

Q: The standard form of the following linear differential equation sin x = (cos x)y + xsin x + 2 is: dx

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Q: dy 3 If , x° + 2xy - y' = 11 find (2, 3) dx by Implicit Differentiation. (so take the derivative and…

A: We have to find the value of dydx(2,3).

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.