Identify whether the differential equation is homogeneous, variable separable, non-exact or exact. Simplify the answer and remove the logarithmic function if possible. 1. (y+sinx-cosx)dy + y(sinx+cosx)dx = 0

Q: (xy² + x²)dy + xydx = 0 %3D

A:

Q: Find constants A and B such that the function y = Asinx +Bcosx satisfies the differential equation…

A:

Q: Determine whether the equation is exact. If it is exact, find the solution. 4 2e³ycosy + y² = c 4…

A:

Q: (16x + 5y)dx + (3x + y)dy = 0,when x = 1, y = –3

A: Given Differential Equation(DE) is a homogeneous DE. Homogeneous DE:    A first order DE in the form…

Q: dªy d²y d³y + dt4 dy + y = 1 dt dt3 dt2

A: Given that, the differential equation is                     d4ydt4+d3ydt3+d2ydt2+dydt+y=1 The order…

Q: Determine whether given differential equation is exact. If it is, find the solution (x + y) dx – (y…

A:

Q: Determine whether the differential equation is exact. If it is exact, find the solution. (7x² − 2xy…

A:

Q: e-(x²+y³)(x dx + y dy) = 0

A:

Q: Determine whether the equation is exact. If it is exact, find the solution. (e*siny + 4y)dx – (4x –…

A: An equation of the form Mdx+Ndy=0 is exact if ∂M∂y=∂N∂xand the solution is given by ∫Mdx+∫Ndy=C  On…

Q: Determine if the given differential equation is homogenous. (x³y³+1)dx + x⁴y²dy =0

A: Given differential equation (x³y³+1)dx + x⁴y²dy =0 Now we will check whether the given differential…

Q: Classify the given differential equation according to its type, order, degree, and linearity. + x2…

A:

Q: Write an equivalent first-order differential equation and initial condition for y. y = 2- |(5+ y(t))…

A: Find your answer below

Q: Find the implicit general solution of the differential equation given. Assume x and y are non-zero.…

A: Given differential equation is dy/dx = (x-4)y^9/x^2(7y^7-y) Use method of variable separable

Q: Verify that the given function is a solution of the differential equation that follows it. Assume C,…

A: given: the function yx=C1e-x+C2ex the differential equation is y'(x)-y(x)=0

Q: Determine whether the differential equation (8x² − 2xy + 6) dx + (2y² − x² + 8) dy = 0 is exact. If…

A:

Q: Determine whether the differential equation (2x² − 2xy + 3) dx + (2y² − x² + 2) dy = 0 is exact. If…

A:

Q: Determine if the differential equation (3x2y + ey)dx +(x3 + xey - 2y)dy = 0 is or is not exact; if…

A: Given problem:- Determine if the differential equation (3x2 y + ey )dx +(x3 + xey - 2y)dy = 0 is or…

Q: Determine whether the differential equation (5x² - 2xy + 6) dx + (7y² - x² + 5) dy = 0 is exact. If…

A:

Q: DETERMINE IF IT IS SEPARABLE VARIABLE, HOMOGENEOUS,EXACT,NON-EXACT DIFFERENTIAL EQUATION?…

A: A differential equation is called separable if it can be expressed as in the form dyf(y)=dxg(x) A…

Q: Consider the differential equation 2t2y" + 3ty' – y = 0. (a) Give the order of this equation. Is it…

A: Linear Homogeneous differential equation with variable cofficients: A linear homogeneous n-order…

Q: Solve the differential equation y' + y == A) y= Inx +cx-² B) y= Inx +cx-1 C) y= In x+cx-2 D) y= Inx…

A:

Q: Given: -x sint = Cc, find the differential equation by eliminating the arbitrary constant a. (cost-…

A: Find your answer below

Q: image attached

A:

Q: Write an equivalent first-order differential equation and initial condition for y. y= -1+ ](5t -…

A:

Q: Evaluate the Particular solution of the differential equation and find y when a = O and x = 2. If…

A:

Q: Determine whether given differential equation is exact. If it is, find the solution. 3y (x² – 1) dx…

A: Let's find.

Q: Determine an appropriate substitution and then solve the differential equation. xy' = y In(xy) Cx-1…

A:

Q: classify the following differential equations according to type, order, degree, and linearity. Also,…

A:

Q: B.Verify if a given function is a solution to a differential equation. 1 d²y dy 1x². +x=y= ln x dx²…

A:

Q: Determine the function y = y(t) that solves the differential equation y' = (t + 1)y² and has y(1)…

A: solution:-  y'= dy/dt

Q: Determine whether given differential equation is exact. If it is, find the solution. (y In y – e*»")…

A:

Q: Classify the following differential equations according to type, order, degree, and linearity. Also,…

A:

Q: Give the order, degree, and identify if the differential equation is linear or nonlinear. m y dx +…

A: Consider the given differential equation mydx+nxydy=0, where m and n are constants. Here, the…

Q: Write the first-order linear differential equation in standard form. xy' + y = x^4 y + 6

A:

Q: Determine whether given differential equation is exact. If it is, find the solution. (1 – xy)*dx +…

A:

Q: Solve for the differential equation of the given function y = C1x + Cze* by applying elimination of…

A:

Q: Solve the differential equation (y4 - 2xy) dx + 3 x2dy = 0. If y = 1 when x = 2, determine the…

A:

Q: Determine whether given differential equation is exact. If it is, find the solution. [3x +y – ye| dx…

A: We will find out the required solution.

Q: Determine whether the equation is exact. If it is exact, find the solution. 3 2exycosy + = C 21² 3…

A:

Q: Determine whether the given differential equation is exact. Show the solution. (xy+ x²)dx − dy = 0

A: To determine:           If the given equation is exact or not=?   So,      The given equation is:…

Q: Determine whether the differential equation xy" - 12y - 32y = 0 s linear or nonlinear and find its…

A:

Q: If the acceleration A(t) of an object is proportional to the square root of its speed S(t); write…

A: In the question we have to write the differential equation of acceleration function.

Q: (y² + 7xy + 16x²)dx + x²dy = 0,when x = 1, y = 1

A:

Q: Determine whether given differential equation is exact. If it is, find the solution. (1 – xy)*dx +…

A:

Q: Determine whether the equation is exact. If it is exact, find the solution. 3 2eycosy + = C 2. 3…

A:

Q: Verify that the given function is a solution of the differential equation that follows it. Assume C,…

A: Given the function is   u( t ) = Ce14t4 where, C is arbitrary constants. Differentiating with…

Q: Determine if the given function is a solution or not a solution of the given differential equation…

A: This question is related to the differential equations, We will solve it using given information.

Q: Determine whether the differential equation is exact. If it is exact, find the solution. (8x² − 2xy…

A: Comparing the given differential equation with the general differential equation Mdx+Ndy=0 we get,…