The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) - y,(x) ==sin(2x)

Q: Show that ¢(x) = Ce³* + 1 is a solution to dy/dx – 3y = -3 for any choice of the constant C. Thus,…

A: We have to check Q(x)=Ce3x+1 is solution of given differential equation.

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: dy sin x 3) dx y=2cos sin x- 1 of first order linear differential equation COSx COsx y(7/4) = 3/2…

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Q: how that the general solution of the differential equation 4z'' - 4z' - 3z = cos2x takes the…

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Q: Solve the second order differential equation ÿ + 3y = x3 + sin x sinx +글stnx +sinx D: y = c,cosv3x +…

A: I am going to solve the given problem by using some simple calculus to get the required result.

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: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

Q: Suppose !=sinh2r, z= 6ư, 3s= cos2r are solutions of a linear homogeneous differential equation with…

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Q: Solve the differential equation. y'+y tan x = cos x, - n/2 < x < r/2 A y = x sin x + c cos x, - 12…

A: Consider the given linear differential equation which is required to solve. Comparing the above…

Q: Q4// Solve the partial differential equation a²u ди cos*x given that = x when y=0 and u=3 when x=0?…

A: The given partial differential equation is ∂2u∂x∂y=cos4x Integrating on both sides with respect to y…

Q: 4. Solve (D-1)y (x'+2x +x+6)e using differential operators method.

A: Consider a homogenous differential equation: ay''+by'+cy=0 Write an auxiliary equation corresponding…

Q: What is of the differential equation (3 +y+ 2y sin² æ) dx + (x + 2xy – ysin2x) dy = 0 ? O 2x sin 2x…

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Q: Find the general solution of differential eqiuation 4 x2y''+y=0 if one of the solution is given by…

A: The differential equation is, . A second order Euler's ordinary differential equation is given by,…

Q: a particular solution that satisfies the differential equation F'(x)=3x^2 +2x -1 and the inital

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Q: (c) )y = 3 cos(x) y' + cos(x

A: We solve the following linear differential equation by using I.F.

Q: How would I solve the differential equations/initial value problems? Please explain each step, it…

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Q: 4. Solve (D² -1)y=(x² +2x² + x +6)e²* using differential operators method.

A: Given D2-1y=x3+2x2+x+6e2x

Q: Show that the solution of the differential equation (1–x*) = 2x(1+ y). dx 1+x given that y=1 when…

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Q: The general solution of the differential equation by direct method: dy sec2 x dx 1+ 2 tanx y =…

A: According to the given information, it is required to find the general solution of the given…

Q: (9x^2 + y - 1) - (4y - x)y′ = 0

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Q: solve the equation using differential equation linear in x and y: (2x-3y-5)dx + (3x-y-2)dy = 0;…

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Q: 4. Solve (D -1)y =(x +2x* +x+6)e" using differential operators method.

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Q: Find the general solution to differential equations 2 #) (-2xy) dx + (Siny-x²) dy +³

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Q: what is the solution to the differential equation 2\sqrt(xy)(dy)/(dx)= 1 at y(4)=1

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Q: Solve the partial differential equation of Lagrange's form  xy2p-y3q=-axz.

A: P p+ Q q=R z We solve partial differential equation by method of Lagrange's multiplier The…

Q: 2) (x²y³ + y)dx + (x³y² – x)dy = o

A: (x2y3+y)dx+(x3y2-x)dy=0 this is an exact equation  M(x, y)= x2y3+y N(x, y) = x3y2-x We will evaluate…

Q: '+y- y²(cos 2x– sin 2x) = 0

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Q: Suppose sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential equation…

A: To find the differential equation :-

Q: 3] Form the partial differential equation by eliminating arbitrary function from z = e® f(x – y) -

A: Given: Z=exfx-y

Q: y' + (2 tan x)y = cos³ x = COS" X

A: The correct answer is option (I) , i.e.  y = (cos²x)(c+sinx) The detailed solution is as follows…

Q: . Given the differential equation: y" = cos(5x). Determine its general solution. A. 125y = -cos(5x)+…

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Q: Find a homogeneous linear differential equation with constant coefficient whose general solution is…

A: Given the solution of a homogeneous linear differential equation with constant coefficient. That is,…

Q: The solution of the differential equation by variable separable method dy (1+ y²) (3x² + 6) 5- is dx…

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Q: Example 4: Form a partial differential equation by eliminating the arbitrary funct from Ix + my + nz…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: 2.) Solve Implicitly 3 (2xy +) dx + (3x³y² + siny) dy =o

A: Here we have to find solution of given differential equation.

Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

Q: What is the general solution with steps of the differential equation y’=sin(3x)y+y+sin(3x)+1

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Q: A solution to the partial differential equation. u u is None cos (3x – y) 2² + y? -3 sin (7x) sin…

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Q: 5) Find a homogeneous linear differential equation with constant coefficients whose general solution…

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Q: 4. Solve (D-1)y=(x'+2x+x+6)e using differential operators method.

A: Given: D2-1y=x3+2x2+x+6e2x

Q: Obtain the solution to the differential equation: (cos'x- cos'y ]dx+ cosx sin 2ydy = 0 a. cos"y(1+…

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Q: 3. (sin'x + cosv)dx - tanxsin2ydy = 0

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Q: The solution to the differential equation -y x cos(3x) - is: Select one: cos(3x) + cx2 O 3x² sin(3x)…

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Q: Find the particular solution of the differential equation (2xy - sin x)dx + (x² - cos y)dy = 0, when…

A: Exact differential equations

Q: The particular solution of the differential equation y y- 2y = sin3x is: y(x) =Ce3x+Ce3O…

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Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx