Solve for the particular solution: dy + 를y3D -2°y"; y(-1) %3D2 dz

Q: . (solve exact de) (2ysinxcosx - y + 2y?e*v* )dx = (x - sin?x - 4xye*)dy

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Q: Solve this DE using Substitution method  (x2+6y2)dx-4xydy=0 ; y(1)=1

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Q: dy Find the solution of 2ху + dx X. 2у-1

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Q: Solve for dy y = sec 2x² dx

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Q: Obtain the general solution to the equation. dy y +7x +1 %3D dx

A: Here we have to find general solution of given differential equation

Q: Solve by Exact method ydx- (2xy +y ²)dy so

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Q: Find the General and Particular solution of = 4y ; y= 3,when x = 0 dx

A: Given: dydx=4y

Q: Solve this DE in Non-Exact method: (x2+6y2)dx-4xydy=0 ; y(1)=1

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Q: (x + у—4) dx — (х — у+2)dy %3D 0

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Q: 4.2(х — у)dx + (3х — у — 1)dy 3 0

A: Let's find.

Q: Solve using Bernoulli's Equation. y(6y^2 - x - 1) dx +2x dy = 0

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Q: Solve for C in the solution for dx/dy = xy^3/(2y^4+x^4) ; y(2)=4 Use 2 decimal places

A: Here we have to solve the given differential equation

Q: (2? + dy = 0 + In y) dx +

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Q: Solve the DE (3xy² – y³)dx +(xy² – 2x²y)dy = 0 %3D

A: Given equation is, ...(1) Let, be the dependent variable then divide by we get, Now, substitute…

Q: The equation dy - ydx = [-x*y^3* e^(-2x) ]dx is linear in x but not in y. True or false?

A: Given that dy-dx=-xy3e-2xdx.

Q: Solve the equation 3(y* + 1)dx + 4xy³dy = 0. (Solution must be clear and concise.)

A: The given differential equation is 3y4+1dx+4xy3dy=0. The above differential equation can be…

Q: Solve: dy dr = y +e*y?

A: The given differential equation is dydx=y+exy2. Rewrite the differential equation as,…

Q: Solve this DE 1. dy/dx+secx(y-2sec3x+2sec2 xtanx) + y cotx = 0

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Q: Find the General and Particular solution of = 3y ; y= 3,when x = dx

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Q: Solve the Linear DE: 2y (y2 - x) dy = dx. %3D

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Q: + 2y = 1- x>0 dx

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Q: 4dx + (x — у + 2)?dy %3D 0

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Q: Q of y = e(cosx+4tanx+5t-tx²) dp

A: We have to find derivative of y with respect p.

Q: Q9// find the general solution (sec³x + (cotx)y)dx + (Insinx)dy = 0

A: Answer and explanation is given below...

Q: Solve the DE: 2 dy 3 dx 3x² + y² xy

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Q: What is the solution? dy/dx - y/x =xy^2

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Q: Solve for the general solution * (eУ — усos ху) dx + (2xe-У — х соs ху +2у) dy %3D0

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Q: Use Picard’s Method with 3 iterations to solve for y(0.1) and y(0.2), the equation dy/dx = x2+y2;…

A: Picard method: Consider the initial value problem, dydx=fx, y, yx0=y0 Then  yn+1=y0+∫x0xfx,yndx…

Q: Find the general solution. dy/dx=15-y y=

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Q: Solve (5 + x²) Y 1 dy dx = x, and verify your solution. *+C Preview

A: Derivative

Q: dy 1- S V9+y2

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Q: Solve for dy when y = + 3x, x=2 and dx =0.5

A: The given problem is related to total differentiation.

Q: Solve the equation by using the method of variation of parameters: d2y dy dx = X 2. dx

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Q: Se"dy 3.

A: We have to solve

Q: 3. 2X dy 2. %3D

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Q: Solve for the General Solution. ( x csc y/x-y) dx + x dy = 0

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Q: Find, the, general solution of 2 dy + y = xe"Inx. dx²

A: Given the differential equation           y''-2y'+y=xexlnx Find the general solution.

Q: d'y dy - -2xe dx dx

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Q: Solve this DE:  (x-y-2)dx + (3x+y-10)dy = 0

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Q: Solve the equation (2y³ – x³)dx + 3x²ydx = 0. correction to the 2nd term: dy

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Q: Determine whether dx = y - x* has a unique solution, for which y(0) = 7

A: To determine: The differential equation dydx=y4-x4 has a unique solution for which y0=7. Concept…

Q: sec?y dx? – csc²x dy? = 0

A: The given differential equation is sec2 y dx2-csc2 x dy2=0, which can be simplified as follows: sec2…

Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy2 - x) dy = 0

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Q: Obtain the general solution to the equation. dx 8 y: + 4x = 9y dy

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Q: Use the method of separation of variables to solve, dy 2x(3x +1) Зу? — 1 dx given that y(0) = 2.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.