Q2\Using the variation of parameter, find the solution of: y'+16y = csc 4x

Q: (x2 + 3 y9 dx - 2xy dy

A: It is homogenous differential equation.

Q: 1. 2ydx + x (²+x²y) dy = 0

A:

Q: solve using Separation of Variables. dy dt = ry-3

A:

Q: y" + y = sec x tan x

A:

Q: Find the general solution for y''=2t+3 by direct integration and by the method of undetermied…

A: Given that      y" = 2t + 3 Here we have to find the general solution by direct integration and by…

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: 2ydx + x(2 + x²y) dy = 0 %3D

A:

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

A:

Q: 2 1 æ sec-(x) dx 2/V3

A: By see this solution below

Q: Solve using method of variation of parameters. 6. y" + 3y' + 2y sin(e*)

A:

Q: x + 4) (y + 1)) dx + (y (x +3x + 2)) đy = 0

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: Find the solution asked using the process of Homogeneous. (16x + 5y)dx + (3x + y)dy = 0; the curve…

A:

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: Q3: Find the general solution for the following Deferential Equations using d²y + y = - sin x…

A:

Q: Use Variation of Parameters to find a particular solution to the non-homogeneous equation y′′−2y′+y=…

A:

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

A:

Q: 3. Find the solution of xydx – (x²+2y²)dy = 0. Use Determination of Integrating Factors.

A:

Q: O y²dx + Cory ty² -Ddy

A: Given y2dx+(3xy-y2-1)dy=0

Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

Q: Solve the DE using Variation of Parameters: y"+y = sec' x %3D

A: Given  The differential equation using variation of parameters. y''+y=sec3x

Q: solve homogeneous equation by linear method Tanx(dy/dx) + y = sec x

A: SOLUTION-

Q: 7) y = exz 8) y = 3 x ²

A:

Q: 44 3) y" +y = sec?x (Use variation of parameter method)

A: To solve the given differential equation.

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* - х)dy %3D 0

A:

Q: 2x5y' = y(3x*+y?) %3D

A:

Q: xy' + y = sin(x), y(3) = 0, y'(3) = 0. Yh = C1x + c2x ln(x).

A:

Q: xydx – (x² + 2y²)dy = 0 ||

A:

Q: Eliminate the arbritrary constant/s. Show full solution. x= -In t, y= at + bt?

A:

Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

A:

Q: 1. y(4x + y)dx – 2(x² – y)dy = 0

A: We will first convert the equation to exact and then solve

Q: Determine the integrating factor in the equation y(8x – 9y)dx + 2x(x – 3y)dy = 0 using the method of…

A: The given differential equation is  y8x-9ydx+2xx-3ydy=0 is of the form y f1x,y dx+x f2x,y dy=0. If…

Q: find the general solution using integrating factor method  dy/dy - y/2 = 2sin(3t

A:

Q: Solve by separation of variables (y +1)dy dx+x(y^2 +2y)= x.

A:

Q: 4. x(x² – y² – x)dx – y(x² – y²)dy = 0, y(2) = 0

A: For the solution follow the next step.

Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: Q3: Find the general solution for the following Deferential Equations using Variation of Parameters…

A:

Q: solve using the method of integrating factors. dy dx ==+x, y(1) = 3 х ||

A:

Q: tion of the separable equation dy 23 3 +2)³ + 2)?

A:

Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

A:

Q: 1. y(x³ – y)dx – x(x³ + y)dy = 0

A:

Q: * 2e² + 6z² – 8z + 6 cosh 3z dz ez + z3 – 2z2 + sinh 3z |

A:

Q: Solve using the integrating factors by inspection and get the general solution of…

A: The given differential equation is, yx2y2+2dx+x(2-2x2y2)dy=0 Now rearrange terms as below:…

Q: Use variation of parameters method to solve b. y" + y = tan x

A:

Q: 3. use "Homogeneous Equations" method (x+y)dx + 2xydy = 0

A: The given equation is x2+y2dx+2xydy=0....(1) Here, we have to solve the differential equation using…

Q: y"+y = e" what is the nonhomogenous(particular) solution of the given differantial equation?

A:

Q: y

A:

Q: dy/dx=x2+3y2/2xy

A:

Q: y' = y sec

A:

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.