4 Give the general solution to x²y' + xy = -2 cos(2x) y¯2

Q: 5. Show that the differential equation y" +a²y = f(x), y(0) = y'(0) = 0, has 1 y(x) = -…

A: proof:-we have          y(x)=1a∫0xf(t)sina(x-t)dt   ⋯(i) differentiate by leibnitz's rule(i) , we…

Q: 8. The differential equation (2x-xy-2y+3}dx-(x*y+2xkty = 0 is exact because ÔM ON

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Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: Show that the first order differential equation (x + 1) y' - 3y = (x + 1)5 is of the linear type.…

A: To solve x+1y'-3y=x+15; y=1.5 when x=0

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: 3) Find the solution of Initial Value Problem dy 2x-sin y dx 2x cos y ; y(4)=0

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

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

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

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Q: 2. Solve the differential equation (3x2 – x³ + 3y – 3.ry – y°)d.x + 3(x + y²)dy= 0, - -

A: Disclaimer: Since, you have requested for a handwritten solution and currently we are not providing…

Q: 3. Form the partial differential equation by eliminating the arbitrary constants a and b from z =…

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Q: 2. Find the particular solution to y " = sin(x) given the general solution y = -sin(x) + Ax + B and…

A: The general solution to the differential equation y''=sinx is y=-sinx+Ax+B

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: 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: ду 9. The differential equation (3ycos.x+4xe" +2x'e" dx+3(sin x+1)dy 0 is exact because ON 10. The…

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Q: Verify that y=2 cos(3x) is a solution to the initial value problem: y"+9y=0, y(0)= 2

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Q: 2. Find the particular solution of sin y(x+sin y) dx +2x² cos ydy = 0 :3(-1) = 2

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Q: Determine an appropriate choice for a particular solution for the differential equation y" + 4y = 3…

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Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

A: Partial differentiation is needed to be done after identifying M and N

Q: 9. Solve the differential equation (2 sin?y + 4x² sin y)dx + (3x sin y cos y + 2x³ cos y) dy = 0…

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Q: (6) Show that the solution of the differential equation dr 3 + dy 3(y + 1) is r (y + 1)³ + c y +1 y…

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Q: Find the largest interval in which the solution of the initial value problem y" + csc(t) y' +…

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Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

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Q: 5. xdy = (y + 2x³)dx

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Q: 5. In the differential equation (1+3xsin ykdx-x cos ydy = 0, we let the substitution %3D

A: Follow the procedure given below.

Q: 2. Solve the initial value problem dy cosz+y sin z = 2z cos²z, y(0) = 5.

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Q: Without solving for the undetermined coefficients, the correct form of a particular solution of the…

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Q: Solve the initial value problem dxdt+3x=cos(2t)dxdt+3x=cos⁡(2t) with x(0)=−1x(0)=−1. x(t)=

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Q: Suppose dr - =4sin(2x) and y= -2 when *=. what is the particular solution to the given differential…

A: In this question, we need to find the particular solution to the given differential equation.

Q: Suppose that x = 0 is a regular singular point of the differential equation x²y" – x(x + 3)y' + (x +…

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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: dy 2. 2xy da 3. 2ydx + x (x² In y – 1)

A: We are asked to solve differential equations.

Q: Show that an implicit solution of 2x sin2(y) dx - (x2 + 19) cos(y) dy = 0 is given by In(x² + 19) +…

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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: 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: 4. Obtain the general solution of x² y2 = dx

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Q: 8 Find the general solution of the differential equation: xy' + y: X Use lower case c for constant…

A: Given : xy'+y=8x+9x Following formulas are used- ∫1xdx=lnx∫xndx=xn+1  n+1

Q: y'+ytan(x)=cos^2(x) ,      y(0)=-1

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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: 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: Find the solution of these differential equations : 1. Cos“ x ax = y + 3 dy

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the particular solution of the differential equation (1-cos(2t))dy/dt=xsin(2t) given that…

A: The given differential equation is 1-cos2t dxdt=x sin2t     with xπ2=2. Solve as follows. 1-cos2t…

Q: 3. Solve the Euler-Cauchy differential equation d²y dy 3x +4y= ln² x – In x dx² dx

A: Given an Euler-Cauchy differential equation, x2y"-3xy'+4y=ln2x-lnx Re-writing it in the standard…

Q: 5. In the differential equation (1+3xsin y dx– x² cos ydy = 0, we let the substitution %3D

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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: 2 sin x Show that y is the solution of the differential equation xy'+y=2 cos x.

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Q: 7. Find the particular solution of the differential equation dx 5x³y = x³ passing through the point…

A: The given question has been solved in detail

Q: Consider the differential equation (10x³y* + e=y + 3 sin(4x + 3y))y' + (6x²y5 + 4 sin(4x + 3y) + 2)…

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