6) f(x) = x³ %3D glx): 2)3 %3D 2.

Q: an integrating factor for the DE dy+ydx=e3x dx is  1)ex 2)x2 3)y 4)x 5)ey

A: To find an integrating factor for the DE dy+ydx=e3x dx

Q: 1. 2ydx + x (²+x²y) dy = 0

A:

Q: Use Euler's method with step size 1 to estimate (¹), where y() is the solution of the problem y +…

A: Given that y'+3x2y=x2 Using Euler's method, find the value of  x at 1. Initial conditions are y0=3…

Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: 2. 2y (x²-y tx) dx-(x²-2y) dy = 0

A:

Q: 2) A: By using partial method solve [2x² cos x dx

A:

Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: Obtain the solution using Integrating Factors Found by Formulas y(y + 2x − 2)dx − 2(x + y)dy = 0

A: Find your answer below

Q: 3. Integration by parts: 3x d x (V3 2x+4

A: To find out the integration.

Q: 2ydx + x(2 + x²y) dy = 0 %3D

A:

Q: y(x* – y²)dx + x(x* + y²)dy = 0

A: Let us consider the differential equation,  Where M and N are the function of  x and y. If the…

Q: A clamped beam of length 3 is modeled by: y(4) = 24, y(0) = y'(0) = 0, y(3) = y'(3) = 0. Solve the…

A: The given differential equation is y4=24, with y0=y'0=0 and y3=y'3=0 Now we integrate the given…

Q: What is the integrating factor of xy' + 6y = 3xy3?

A:

Q: Xe dx (x + 1)² 4.

A: Given that, 4.∫xexx+12dx Used formulas: ∫u du=uv-∫v du

Q: In x 2. Integrate -dx , (i) using the sub stitution u = Inx (ii) using integration by parts.

A: Integrate by substitutions and by parts

Q: 2. у(у+ 2х — 2)dx — 2(х + y)dy 3D 0

A: A differential equation of the form M(x,y)dx+N(x,y)dy=0 is said to be exact iff, ∂M∂y=∂N∂x

Q: Obtain the General Solution (x-1 )dx - (3 x -2y -S) dy = 0 MAM

A:

Q: Find the general solution for y' = x – 4xy using an integrating factor.

A:

Q: x³y³dy у2— 4у-21 (x – x4y)dy + (y + x³y²)dx :

A: See the solution and follow the step.

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate (x' + 1)dx.

A:

Q: Obtain the solution using Integrating Factors Found by Formulas a.)  xydx − (x2 + 2y2)dy = 0

A: I am attaching image so that you understand each and every step.

Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

A:

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

A:

Q: 7. Integrate em***)dx_using the Substitution method. x +3

A: To evaluate the given integral using substitution method.

Q: Obtain the solution using Integrating Factors Found by Formulas. 2(2y2 + 5xy- 2y + 4)dx + x(2x +…

A: We can solve this using integrating factor

Q: O y²dx + Cory ty² -Ddy

A: Given y2dx+(3xy-y2-1)dy=0

Q: solve the Initial Value Problem using Separation of Variables. y' = xy2, y(1) = 2

A:

Q: What is the value of the coefficient d of the equation y = ax + bx² + cx + d so that it will have…

A:

Q: xydx – (x² + 2y²)dy = 0 ||

A:

Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

A:

Q: Obtain the solution using Integrating Factors Found by Formulas. xydx - (x² + 2y²)dy = 0

A:

Q: Solve integration by (udv) T/2 DS Š X cos(x) dx 2) { X cos (ux) dx 7/2

A:

Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

A: We have dydx=3y Now, we can write this as: dyy=3dx Now, integrate both sides: ∫dyy=∫3dx⇒lny=3x+C…

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

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

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

A:

Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

A:

Q: Obtain a numerical solution of 2y + y - x=0 using Euler's method with step size equal to (0.5) and…

A:

Q: The integrating factor of the equation (2 + y + x) dx + xydy = 0 is

A:

Q: solve the Initial Value Problem using Separation of Variables. y' = cos2x, y(0) = π/4

A:

Q: Find the Bolution to the initial value problem. | -y = 2€ %3D %3D

A: Given IVPy'''-y'=2e-t+9e2t  ; y(0)=0 ,  y'(0)=-1   , y"(0)=2 to find the the general solution use…

Q: What is the integrating factor of the linear De of order one ydx + (2 – xy)dy= 0 ?

A:

Q: 3. Integrate! 12e-0.21 а) -dt b) 6r 3,2 Se041 dr dx c) f- x. V1+ In 3x?

A:

Q: Pydx + x(2 + x²y) dy = 0

A: Topic:- differential equations

Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: (2x² + y)dx + (x² – x)dy = 0

A:

Q: What is the integrating factor of 6y²dx – x (2a + y) dy Oy-2 Oy? Oy

A:

Q: | (In x)2 dx Use integration by parts.

A:

Q: Show that the antiderivatives are equivalent.…

A: ∫6/(4 + 9x2)  dx = arctan 3x2 + C or arccsc √(4 + 9x2 ) / 3x + C We need to show that the…