Q1) A: Solve the differential equation: x- y = x.cos? ? dx B: Evaluate the following integral by changing the order of integration: (2 (x+2 dy dx

Q: What could be an integrating factor in solving the differential equat (х2 — 4у — у? — 1)dx + 2x(у +…

A:

Q: Solve the given differential equation by variation of parameters. x2y" + xy' – y = In(x) y(x) = ,x >…

A:

Q: Solve the given third-order differential equation by variation of parameters. y" + y' = cot(x) y(x)…

A:

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: To determine the general solution of the differential equation.

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given differential equation

Q: Find the general solution of the given differential equation, and use to determine how solutions…

A:

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: The given differential equation is dydx=x3y. Solve as follows. dydx=x3yydy=x3dx

Q: Solve the differential equation by variation of parameters. 4y"8y' + 8y = ex sec x y(x) =

A:

Q: Use the integration to find the general solution of the differential equation dy = 3x². dx

A:

Q: Solve the differential equation by variation of parameters. 2y" — 4y' + 4у %3D е* sec x y(x) = %3D

A: Solution is given below:

Q: For the differential equation x ^ 2y ”+ xy’ + y = 0, check that y1 = cos (lnx) is a solution. Find…

A: According to the chain rule of differentiation, the differentiation of the composite function…

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: Given : differential equation            6y'+y=7t2 To find : general solution of the given DE and…

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: We know that , A first order linear differential equation has the form ,  y' + Pt y = Qt  We have…

Q: Find the general solution of the differential equation. (Use C for the constant of integration.)…

A:

Q: Find the general solution of the differential equation y" – y – 2y = cosh(2t). %3D et + e-t NOTE:…

A: Give differentiate equation is y''−y'−2y=cosh2t We have to find the general solution of the given…

Q: 3. State the order of homogeneity and solve the differential equation as a homogeneous equation. х…

A: The objective is to state the order of homogeneity and solve the differential equation as a…

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A:

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: We have to solve the given differential equation. Also find the value of y as t tense to infinitive.

Q: (x – 2y + 3)dx + (4x + y + 3)dy = 0 %3D

A:

Q: Use integration to find a general solution of the differential equation       dy/dx = 8 csc x cot x

A: Given: dydx=8 cscx cotx

Q: (x- cnoy) dx - siny dy =o 1-) solve the differential equation by finding an integration factor?

A:

Q: Solve the given third-order differential equation by variation of parameters. y"" + y' = cot(x) y(x)…

A: To find- Solve the given third-order differential equation by variation of parameters. y''' + y' =…

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: The given differential equation: dx=x9y dy

Q: Use separation of variables to find the general implicit solution to the differential equation. 9…

A: Given:       9 dydx=eysin2θysecθ

Q: use an integrating factor to solve the given differential equation. dy 5x 4y = Ce - dx

A: Use the mentioned method.

Q: 7.) (y sec² x + e cos x – xe³ sin x) dx + (xe³ cos x + tan x) dy = 0

A: Recall: In an equation of the form Mdx +Ndy=0 , first check the condition of exactness i.e, ∂M∂y…

Q: dy = (x – 3y)dx

A: The given differential equation is: dy = (x-3y)dx We need to find the integrating factor for the…

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: If y=f(t), then the independent variable t is called the input of the function, and the dependent…

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Consider the given D.E. Rearrange the D.E.

Q: 4. Solve for the general solution of the differential equation using homogenous equation. [x cos?…

A: A homogeneous differential equation is an equation containing a differentiation and a function, with…

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A:

Q: Find the general solution of the differential equation y" – y – 2y = cosh(2t). - et + e- NOTE:…

A:

Q: Solve the given differential equation by separation of variables. csc(y) dx + sec (x) dy = 0 (2x +…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A:

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A: First Solve differential equations ,

Q: Find the general solution of the differential equation: e- lt tan x - lx y' + 3y : Leave the answer…

A:

Q: 34. cos x dx + (1 + + - sin x dy = 0

A:

Q: Solve the differential equation with the initial condition: (a) = 3t2 + cos t, y(0) = 12, (b) = sec?…

A:

Q: 4. Зx2! x3 8(у + 1) %3D 0 y+1

A:

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: To get the general solution , put all the y terms together and x terms together

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A:

Q: 5. dy = (x³ – 2xy)dx %3D

A: The solution is given as

Q: What is the suitable formula to solve differential equation using method of integration factor? A.…

A: This method is used to solve 1st order linear differential equation.

Q: Solve the differential equation by variation of parameters. 3y" 6y' + 6y = ex sec x y(x) =

A: Given :  A differential equation 3y''-6y'+6y=ex secx. To find : The solution of a differential…

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given a differential equation, dx=x6y dy

Q: Solve the given third-order differential equation by variation of parameters. y" + 64y' = sec(8x)…

A:

Q: Is the y=2 cos(x) is the solution of the differential equation of yy' + 2 sin 2x=0? Solve and…

A: In this question we have to find is the y=2cos(x) is the solution of the differential equation of…

Q: Find the general solution of the differential equation. (Use C for the constant of Integration.) dy…

A:

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: Given Equation 8y'+y=8t2y'+18y=t2 Comparing with standard form y'+Py=Q P=18Q=t2