4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

Q: C. Solve the nonhomogeneous ODE. y" + 2y' + 5y = x² + cos3x

A: To solve the following differential equation  y" +2y' + 5y = x2 + cos3x

Q: Express the equation r = 3 cos 0- 12 sin 0 in Cartesian coordinates. (x² + y²) – 3r + 12y = 0 + y²)…

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Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: Solve the following exact equations: 1) (сos 2y — 3x*y*dx + (сos2y — 2xsin 2y -2x'y)dy %3Dо 2) (2ху-…

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Q: 1. Find the general/particular solution of the following linear equation at first order. a. x²dy -…

A: Given : The following are the three linear equation of 1st order a  x2dy-sin2xdx+3xydx=0b…

Q: Solve the given DE: dy ex – 2x cos y ey – x² sin y' - dx

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Q: Obtain the general solution of the following equations: sin y(x+sin y)dx+2x2cos ydy=0

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Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2e sin2(x/2)

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Q: dy 2y ! = -x² y² sec²x %3D dx +

A: Using solution of Bernoulli Differential equation.

Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(9y) dy = 0,…

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Q: Find the particular solution : y" + y' + 16y = cos4x (a) yp = -4sin4x Yp =sin4x (b) %3D %3D (c) yp =…

A: The correct option is b i.e. yp=14sin4x i.e. 14sin4x is the particular solution of the differential…

Q: Find a particular solution of the equation y2y' = cosx satisfying the initial condition y(0) = 0.…

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Q: Solve the IVP (1/x + 2y^2x)dx + (2yx^2 - cos(y))dy = 0, y(1) = pi. Give an implicit solution.

A: Consider the differential equation 1x+2y2xdx+2yx2−cosydy=0.........(1) Compare the equation (1) with…

Q: show that the solution y(t)=e^2t(cos(t)-2sin(t)) is linearly independant.

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Q: Find a particular solution yp for the equation. y" - 6y' + 5y = cos3x 3sin3x

A: Consider a non-homogeneous differential equation of the form a(x)y''+b(x)y'+c(x)y=r(x). Then the…

Q: Suppose we are given y₁ (x) and y2(x) (with y₁ y2), which are two different solutions of a…

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Q: 2x Show that y = e²* sin 3x satisfies the equation y"-4y'+13y=0.

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Q: 3. Describe whether the first order type: Linear or Exact and then solve to find the general…

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Q: Find the general solution of (y + 2y) sin r²dr + V1 dy = dp. 0. %3D

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Q: Solve the given DE. (D² – 3D + 2) Y 1 cos² (e¬²)

A: Differential equations, method of variation of perameters

Q: Find the solution to the Bernoulli equation. y = 2(3x+ y)2 – 1; x= 0,y=1 O 4tan-1(3x+ y) = 8x + T…

A: The solution is given as

Q: Find the general solution of the following equations. 4. dy - x² = x dx sin x 5. y-'dy + ye cos x dx…

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Q: . Find the qeueral solution: - 2 dy +5y = ex Cos 2x

A: Complete solution = complementary function + particular integral.

Q: (c) y" + 2y-3y = 9 sin(t)

A: A detailed solution is given below

Q: 2x Find the general solution of y" – 4y' + 5y sin (2)'

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: Match the equation to the graph. y 2 sin 30 - 1 %3D Sn / 3n 7n 21 4.

A: y=2sin3θ-1Use the form  a sin ( b x − c ) + d  to find the variables used to find the amplitude,…

Q: (g) The solution of y' + (2/t)y (cos t)/t², y(7) = 0, t > 0, is Y COS (sin t)/t².

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Q: (cos t)y" + (sin t)y' – ty = 0,

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Q: (a) Solve the equation, = 4e cos 2x subject to the boundary conditions that dxdy d?u du at y = 0, dx…

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Q: Find the solution. (D2-4D +7)y = 0 y = e-2(c,cos3x +c,sin3«) Oy= e"(c,cos/Zx+c,sin/2x) O y-…

A: Given differential equation is (D2-4D+7)y = 0

Q: FIND Y(s) OF THE GIVEN EQUATION. y" + 4y = cos(t-3)+4t, y" - 6y + 15y = 2 sin(3t), y(3)=0_y' (3)=7 y…

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Q: 8) Find the general and particular solution for the following separable equation dy -.5y, y(0) = 2…

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Q: . Find a particular solution to the inhomogeneous equation y" – 9y/ + 8y = e* in the form y(r) = c-…

A: To find A particular solution to the inhomogeneous equation in the form y(x) =Ce^(2x)

Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

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Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

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Q: 1. Solve the nonhomogeneous equation by using the method of variation of pa- rameters. d'y dy + 2y =…

A: Given differential equation d2ydx2-2dydx+2y=excosecx. The objective is to solve the equation by…

Q: Find the solution to the Bernoulli Equation. (3siny-5x) dx + 2x² cotydy=0

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Q: 3. Solve the DE: 1 + 2.ry? ) dx + (2ya² – cos y) dy = 0, y(1) = || - -

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Q: Find the complete solution of d2y/dx2 + 2dy/dx + y = sin x cos 2x.

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Q: 4. Show that 3x²e"dx + (x*e" – 1)dy = 0 is an exact equation and then find the solution.

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Q: What is the solution of D.E (D2 - 2D)y = e sinx when solved using the method of undetermined

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Q: Find the general solution: y" + 5y' + 6y = 4e¬t cos2t + sin2t A - BI -

A: Differential equations

Q: y" + 9y = e" cos 3x + x² + x³e*

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Q: (b) d²y dy Find the solution for cos(x) ² − (1 + x²) dx − 2xy = 12 with the conditions - dx² dx 1+x²…

A: Given cosxd2ydx2-1+x2dydx-2xy=11+x2y1=-1, y2=2, h=0.25`

Q: Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos…

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

Q: Use undetermined coefficients to find the particular solution to y" + 4y' – 5y = – 1360 sin(3t) %3D…

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

Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0.

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Q: Find the general solution y" +4y'+5y=2e +cos.x -2x

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Q: Solve the following a) 2d²y_dy 3y = 25 sin 2x dx² dx d²y b) - 4 - 3y = 25 sin 2x dx² dx c) d²y dx² +…

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