5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

Q: What is the general solution to the differential equation (tan x)dy - (4y In y - y tan³x)sec²x dx =…

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Q: The solution of following Differential Equation dy sec²y+x tan y = x³ , is %3D dx

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Q: find ƒx , ƒy  . 1. ƒ(x, y) = ln (x + y) 2. ƒ(x, y) = sin^2 (x - 3y)

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

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Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

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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: Show that y = cos xsin x is the solution of the differential equation y'+y tan x cos x

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Q: Consider dy – y sin(3x) dx = 0, y(0) = 1, x € [0,1] a) solve this problem using RK4 with step sizeh…

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

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Q: I. FIND THE GENERAL SOLUTION OF THE FOLLOWING DIFFERENTIAL EQUATIONS: tan xdy (x tan x+ In y)dx 0 =…

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Q: dy Determine the general solution of = 1+ 3y tanx. dx

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Q: 15. cos y sin 2x dx + (cos2 y cos²x) dy = 0. cos² x(1 + sin y) = cos y(y + c - cos v). ANS.

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Q: 04- Determine the general solution of the following differential equat dy tan x. +у %3D sec х dx

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Q: Find a particular solution of the differential equation COS X dy dx 1 +ytanx = cos x e cos x for…

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Q: Verify that y=sinx is a solution to dx dy 2cos x-sin x+y and solve the 2 cosx differential equation…

A: Given Information :  Differential equation : dydx = 2cos2x - sin2x + y22 cosx  y1 = sinx y(0) = -1

Q: dy tan tan x = 0 dx coscos x +

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Q: y' + y² = 3y tan x tan? x + 1

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Q: c) Find the solution of the differential equation +y tanx = cos²x which satisfies the following…

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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: 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 particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: Solve for the DE: (y²-1)dx + (2xy- Siny) dy =0 When x= -1 ; y= 0

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Q: Find constants A and B so that y = A cos(x) + B sin(x) satisfies the differential equation y" + y' –…

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Q: -Solve Bessel's Equation of order zero point x = 0 + xy = 0 around

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Q: 1: Find general solution of D.E. dy cosh (x) + sinh(x) y = e* dx

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Q: Bernoulli’s Equation xdy − ydx − xy^3dx − xy^3 ln xdx = 0

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Q: What is the solution of the equation dey/dx=y/x+tany/x

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Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: Explain why the initial Value problem dy/dx=x-cos(y); y(1)=pi has a unique solution. For that…

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Q: The differential equation (3ycosx+ 4.xe* +2x'e" dx+ 3(sin x+1)dy 0 is exact because OM ON Ox

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Q: 5. With the substitution cosy == differential equations sin y dy – cosy(1 – x cosy)dx=0 reduced to a…

A: Substitute  cosy=1tNow differentiate it with respect to t,-sinydy=-1t2dtsinydy=1t2dt

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

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Q: 10. What is the integrating factor of the differential equation * y = csc a-ycot a tan a sec x O…

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Q: zln x dx 2) S 3 cos3 x sinó x dx 3) 12.1 dt 13. 3t + 2

A: Explanation of the answer is as follows

Q: 2. (2.xy – sin x)dx + (x² – cos yldy =

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Q: If the integrating factor of the differential equation dy + py = q is sec³ x ,then the value of the…

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Q: Consider P(D)y = 0. What conditions on the rootsof the auxiliary equation would guarantee that…

A: Solution: Consider the given Differential Equation P(D)y = 0 Let the Auxiliary Equation of given DE…

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: 1 Solve for the differential of y when y=sinzx, x=÷, and dx= - 3 A) B) 2 -- C) D)

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Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: Given differential equation:(tanx)dy-(4ylny-ytan3x)sec2xdx=0To find: General solution of the…

Q: HW 0If y=tanx show that- yl" =-2 Siny coży

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Q: 5. a) Determine whether the given differential equation is exact. (sin. x)" dy 1+cos y = 0. dx

A: Given: sinxdydx+1+2xcosy=0

Q: Find dy/dx for the following : 1) y = x + sin x² + stn-! 5x 2) y = 32x + In (stn x²) + In(sin-1 5x)…

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Q: 1 Solve for the differential of y when y=sinx, x=÷, and dx=-

A: Solution. A is true.

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

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Q: What is the general solution to the differential equation (tan x)dy – (4yIn y – y tan³x)sec?x dx = 0…

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Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…