3.6da =-ka 3-b. dt Solve the differential equation and Express the x as a function of trigonometric function

Q: Q.2: Solve the higher differential equation below; yiv – y = 2 cos x

A: yiv-y=2cosx The above differential equation can be written as D4-1y=2cosx      , D=ddx The Auxiliary…

Q: 6. Solve the differential equation by using the method of variation of parameters: y"+ y = sec x…

A: The general solution of the second order linear differential equation y''+py+qy=fx is y=yc+yp where…

Q: Find the value of k so that the given differential equation will be exact

A:

Q: Q4- Solve the following differential equation: (1 + x²) dy + (y - tan-¹(x)) dx

A:

Q: Solve the given differential equation by separation of variables. dP = p - p² dt P ||

A:

Q: ordinate at x = 3. 36. Solve the differential equation (x-2)(x+3)-- (2x+1)3D0 given that y= In6 when…

A:

Q: 4. Which of the following represents the differential equation of the family of parabola having…

A: Follow the procedure given below.

Q: 4. y = Cie+ C2e + Cse, where y(0) =0, y'(0) = 1, y"(0) = 2 %3D

A:

Q: For what values of r does the function y= e™* satisfy the differential equation y"- 4y'+ 2y = 0?

A: for the homogeneous differential equation, the auxiliary equation is  compare this equation with…

Q: 5. Solve the given differential equation. (Recommend using Variations of Parameters) y"+3y'+2y =…

A: Given that, the differential equation is y"+3y'+2y=sinex. Obtain the complementary solution.…

Q: Solve the differential equation given below 3y2(dy/dx)+y3=e-x

A: We have to solve given differential equation:

Q: 3. Solve the following higher order differential equation given that y() = 0, y'() = 2 [Apply the…

A: Recall: If the root of Auxiliary equation are complex (say) α±iβ then complete solution is…

Q: The differential equation of the form = sin x has a degree equal to dy %3D Enter your answer as a dr…

A: We have to find out degree

Q: Bernoulli Equation xydx+ (x ?-3yJdy

A: Given xy dx +x2-3ydy=0xy+x2-3ydydx=0xy+x2-3yy'=0

Q: y' = 2y + x(e3x – e2x) y(0) = 2 %3D

A: To solve the following problem by 4 step   Find yc Find p.i. yp  The general solution = yc + yp…

Q: 6. yi + y = 1, when x = 0, y = 4 %3D dx

A:

Q: Q-7. Solve the differential equation y = 1+ fip +..... for | 1 |< 1. dz dz

A:

Q: 5. Find the solution, using variation of parameters, to the differential equation (D³ + D)y = sec²x.…

A:

Q: y > Ae* +Be* +ce; A,B and c unstant are

A: As per our guidelines we can solve only one question at a time please upload unsolved question…

Q: The following differential equation satisfies the following initial condition y(0)=-3. ydy-xdx-0…

A:

Q: Consider the following differential equation to be solved by variation of parameters. 4y"-y = eW/2 +…

A:

Q: 3. (D² + 4)y = 10 cos 3x. ANS. Y = -2 cos 3

A: We have to find solutions

Q: 8. Solve for the general solution of the differential equation using linear equation y' = csc x- y…

A: To find the general solution of the differential equation using linear equation.

Q: Q2 Form a differential equation from the function y = (4– 2 cos x) x)cosx.

A: Given below the detailed solution

Q: 2xy' 2 tan(y) + (y')' (cosy)²

A: According to the given information, it is required to find the general and singular solution of…

Q: 7. x = A + By + Cy² + De-4y; xV + 4x"' = 0

A:

Q: Consider the following differential equation to be solved by variation of p y" + y = csc (x) ind the…

A: The solution is given below

Q: 2y 4. у'+ х+1 = (x + 1} %3D

A: 4) Here we have, y'+2yx+1=x+12 Compare with, y'+yp(x)=q(x)

Q: Q1. Show that the given function is a solution of the differential equations. y = e-* + sinx y" + y…

A: Given differential equation                                              y''+y=2e-x    or…

Q: 3.(i) Solve the Non-linear differential dy 1 - x2 equation 4· XVG da

A:

Q: Consider the following differential equation to be solved by variation of paramete y" + y = csc(x)…

A:

Q: 1. Solve the first order linear differential equation. dy --(cot x) y = sin' x dx

A:

Q: Solve the given differential equation by separation of variables. dN + N = Ntet + 3 dt

A:

Q: 5. Find the general solution of the differential equation using GeoGebra (D² +9)y=2 sina

A: General equation of differential equation.

Q: Given, (+) dz + (41) dy =i0 an exact differential equation. Az+1 Determine the value of A.

A: This question is related to exact differential equations, we will solve it using the condition for…

Q: Q4: Find the general solution of the differential equation y'+ (tan x)y = sec2 x %3D

A:

Q: (5) Solve the differential equation by variable separable z sin ydy = (r'e* In z+ ze")dr

A:

Q: Consider the differential equation y" – (2+ a)y + 2ay = 0 find the value of a that would give double…

A:

Q: 5) Solve the differential equation given as dy (dz) ² dy +2- y dr² dr

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Q: 2xe2"dy + (e?y – 12x?)dx = 0

A:

Q: Determine (a) the order, (b) the unknown function, and (c) the independent variable of each of the…

A: We have, the following answer to the problem.

Q: 2. The degree of the differential equation 5x +Sy =0s dr

A: We will find the degree of differential equation in the following step.

Q: (2x sinh + 3y cosh?) dx -- 3x cosh?dy = 0

A:

Q: The differential equation formed by eliminating arbitrary constants a and b of y = 9 a sin z + b

A:

Q: a) Predict if the following differential equation is exact or not. Hence solve it. dy xy-cos xsin x…

A:

Q: 3. Solve the differential equation by variation of parameters. y" + 3y + 2y = cos(e*)

A:

Q: A (플) n (2프) %3D Cos dt?

A: This is the problem of differential equation.

Q: dy _ху + Зx — у — 3 - - 19. dx ху — 2х + 4у — 8

A:

Q: 2. Solve the differential equation dy 2y-cot x tan dx

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.