Verify that y=sinx is a solution to dx dy 2cos x-sin x+y and solve the 2 cosx differential equation using the initial condition y(0)=-1

Q: Solve the differential equation: sin(2x)cos(y) − sin(y)sin2(x)dy/dx = 0

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Q: Verify that the function y = 6x − 4 sin x + 1 is a particular solution of the differential equation…

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Q: sinx dy = 0 y cos xdx + 1+

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Q: 3. Find the general solution of this separable differential equation. dy y cos x dx sin x + 2

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Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: Find afunction yp that is a solutionto the differential equation,y′′+y′=2e2x+cos(x).

A: To find the solution y"+y'=2e2x+cosx

Q: Solve the first order differential equation dy ycos' x 1+ sin x dx

A: The given equation is first order, linear differential equation.

Q: 5. Find the general solution for the differential equation -(sin y + y sinx )dx + (cos x – x cos…

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Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: 5. Cx sin y +x²y = Ay

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Q: Use the initial condition to find the particular solution of the differential equation. dy = 4xy…

A: In the given question apply the variable separable method, i.e, isolate the y terms on the left side…

Q: 2. Obtain the Differential Equation from the given general solution. y = Cj cos(3x) + C2 sin(3x) +…

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Q: Obtain a linear differential equation with real, constant coefficients that is satisfied 1 sin 2 1…

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Q: Solve the non-Linear differential equation cOS y dy = sin y(1 – O sin y).given that y(0) = 4.

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Q: Solve for the general solution of the differential equation using homogenous equation. [x cos² (y/x)…

A: We will write the general solution.

Q: y cos x dx+dy=0 y

A: Given query is to find the solution of the differential equation.

Q: 2. (cos x cos y cot x) dx + (- sinx sin y) dy = 0

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Q: Find the differential equation by eliminating the arbitrary constant  sin-1x + sin-1y = c

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Q: Find the solution of the differential equation tan x dx +tan y dy=0.

A: Here we have to find the solution of the differential equation  tanx dx + tany dy = 0.

Q: Solve the differential equation (ey+)cos x dx+ey sin x dy=0

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Q: sin y(x + sin y)dx + 2x cos ydy = 0

A: Given: sinyx+sinydx+2x2cosy dy=0Bernoulli's equation:dydx+pxy=qxynLet v=y1-nLinear differential…

Q: Solve the differential equation by variation of parameters. y"+y = n²(x) xx) = c₂cos(x) + csin(x) +…

A: The solution is given as

Q: Show that the solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is  1+tan(x+y)/ 2 =…

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Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation: y'x=4tan2x-3cosx Here, the objective is to find the…

Q: Find the implicit solution of the differential equation (1+sin(y))dx + (1+x cos(y))dy = 0.

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Q: The standard form of the differential equation cosx y' + cosx y = x sin x is: None of the above O…

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Q: 2. Solve the differential equation using undetermined coefficients satisfying the given conditions.…

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Q: 4. Consider the differential equation dy arctan r sin(ry). dx (a) Find all equilibrium solutions.

A: From the given information. The differential equation is as follows.

Q: The solution of the exact differential equation (²+y' cos x)de+ (2xy+3y sinx)dy=0 is:

A: The given equation is y2+y3cos xdx+2xy+3y2sin xdy=0 The given equation is of the form Mdx+Ndy=0…

Q: Find the solution of the differential equation dy = cos(5x) Vy dx which satisfies the initial…

A: y'=cos5xy dydx=cos5xy dyy=cos5xdx y-12dy=cos5xdx take integration

Q: Solve the separable differential equation. dy (1+y²) coshx dx 9+sinh x

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Q: y" +y = cos x ; when x = = 0, y = 0,y' = 1 %3D

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Q: 3. Solve the Euler-Cauchy differential equation d' y dy - 3x+4y=ln² x – In x dx dx?

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Q: Use the method of undetermined coefficients to find a particular solution to the differential…

A: Explanation of the answer is as follows

Q: Show that the function y=ex(sin2x+cos2x) is a solution of the differential equationy′′−2y′+5y=0.

A: We find the first two derivatives of y using the product rule

Q: Find the general implicit solution to the differential equation xy2 cos(x)dx + 2xy sin(x)dy = 0.

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

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Q: Solve the non-Linear differential equation dy Cos y de sin y(1 – 0 sin y),given that y(0) = 8.

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Q: 9. The differential equation (3y cosx+4xe" + 2x'e' dx + 3(sin x +1)dy=0 is exact because aN

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Q: Solve the differential equation dy/dx =(3x^2 - sin⁡ y)/x cos y.

A: By using exact diff equation

Q: Solve the differential equation as follows: (6xy* – sin x tan y)dx + (12x²y³ + sec? y cos x – 5y²)dy…

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Q: 3. (cosy + ycosx)dx + (sinx – xsiny)dy = 0

A: Given: cosy +ycosxdx +sinx-xsinydy =0 ⇒cosydx +ycosxdx +sinxdy-xsinydy =0

Q: The solution of the differential equation using dy = 5/1- y? dx variable separable is cOs 5х + с O…

A: Solve by variable separable

Q: The differential equation (3ycosx+ 4xe* + 2x²e* ]dx + 3(sin x + 1 )dy = 0 is exact because ƏM ƏN

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Q: Obtain the solution of the differential equation (3 sin y − 5x)dx + 2x^2cot y dy = 0

A: Given the DE is 3siny-5xdx+2x2cotydy=0.

Q: 1. Solve the differential equation dy y²sin(2x)sin²(x) = 0, y(0) = 1 dx - %D

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Q: Use the initial condition to find the particular solution of the differential equation. Differential…

A: In this question, separate y terms in LHS and x terms in RHS and then integrate both sides to get…

Q: dy 47. = cos cos 2x, y(0) = 3 dx

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Q: Verify that the function y (cos( 6x)) is a solution to the differential equation y = 6 sin(6 9e

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Q: Solve the differential equation dy – y² sin(2x)sin²(x) = 0, y(0) = 1 %3D %3D - dx

A: Given that: dydx-y2sin(2x)sin2(x)=0, y(0)=1

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.