y(4) – 16y" = e¯* + sin3x y

Q: 2. Solve Bernoulli differential equation of y' + xy = xy².

A: We need to solve the differential equation.

Q: The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and…

A: To solve this differential equation, substitute y'=u

Q: Find a suitable form for particular solution of the differential equation y5) + 25y3) = 5 – tešt +…

A:

Q: Help

A: In such problems ie second order linear differential equations when we are given one solution,y1 we…

Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Find the general solution of the first-order differential equation                       y′ = 2x√(1…

A:

Q: Solve for the non-homogenous linear differential equation: y''+4y=cos^2(x)

A: Given; y''+4y=cos^2(x)

Q: The solution of the differential equation In(y')=2x-y is given by

A:

Q: Find the general solution of the first order differential equation (x+2) y′ + 4y = (3x + 6)-2 lnx.

A: Given: x+2y'+4y=3x+6-2lnx for finding solution of given differential equation, first we convert it…

Q: The particular solution of the following nonhomogeneous differential equation y"-2y' +y = x² +e-* by…

A: Given nonhomogeneous differential equation:y"- 2y'+ y= x2 + e(-x)  ;

Q: Find general solution of the Euler differential equation x2y” + 3xy’ - 3y = 0

A: x2y” + 3xy’ - 3y = 0

Q: Show that the function  y1=x-1 is a special solution of the differential equation y'=1-(y-x+1)2 and…

A:

Q: Find the general solution of the first order differential equation 2xy(dy/dx)=x2-y2

A: The given differential equation is a homogeneous. See attached file for a step by step explanation.

Q: find the general solution of the first-order linear differential equation. y' + y = ex

A:

Q: Find a linear differential equation with constant coefficients satisfied by e² ³x, and e4x

A: A linear differential equation having auxiliary roots m1, m2, m3,....... have following independent…

Q: Find the general solution of xy' + y = y2lnx Bernoulli's differential equation.

A:

Q: Find a general solution of the second-order nonhomogeneous differential equation y" - 2y' + y =…

A:

Q: One solution of the differential equation y''+y'=0 is y=e^-x. A second linearly independent solution…

A: We will find out the required solution.

Q: Find the general and Singular Solution of the following differential equation y=2PX-P²

A: To Find:  General and singular solution of the following differential equation :      y = 2px - p2

Q: 1 Verify if y = -+; xy + y = x² is a solution of a differential equation.

A: We have to verify the solution

Q: Find a particular solution yp of the nonhomogenous differential equation y(3) + y' = x sinx + x²e* +…

A:

Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

A: Given differential equation is y''-y'-2y=2 e-x   Let the particular solution of this differential…

Q: Show that the differential equation UTM dy -2 - ye rey - 2y dr is exact and find its solution.

A: Use the concept of exact differential equations.

Q: By using suitable method, form an ordinary differential equation by eliminating constant A from the…

A:

Q: find the solution of the z'=xz'' - e^z'' differential equation.

A: The differential equation is z'=xz''-ez''                            ......(1) Let dzxdx=vx, which…

Q: y' = y + y3

A:

Q: 4y" + y' = 0

A: We calculate differential equation by the help of Euler identity

Q: Find the general solution of the first-order differential equation                       y′ cos x2 +…

A: The first-order differential equation is y'cosx2+ycosx2x=secx2

Q: Find the general solution of the first-order differential equation                    (2y − ex) dx +…

A: Given first order differential equation is 2y-exdx+xdy=0 for x>0. To find the general solution.…

Q: Use the method of Undetermined Coefficients to find a PARTICULAR SOLUTION to the differential…

A:

Q: The particular solution of the following nonhomogeneous differential equation y" – 2y' + y = 4x² +…

A: y''-2y'+y=4x2+ex This has characteristic equation               λ2-2λ+1=0λ-12=0λ=1…

Q: Obtain the general solution of the given differential equation using the appropriate method. y' = y…

A:

Q: Consider the Non-Homogenous differential equation: y"-y= 6sinx Given that y. = Ce* + Cze-*, using…

A: Suppose we have second order linear differential equation as .  Consider are independent solutions…

Q: Find every nonzero solution of the differential equation y = y +2y°.

A:

Q: use the method of variation of parameters to find a particular solution of the given differential…

A: solution:-  The given differential equation is  y''+4y=cos3x The auxiliary equation of above…

Q: The particular solution of the following nonhomogeneous differential equation y" - y' - 2y = 4x² +e*…

A: Here  Particular solution is in the form  yp(x) = Ax2 + Bx + C + De-x

Q: The solution of the differential equation y^'=-2xy is a family of solutions of

A:

Q: 6, find the general solution of the given differential equation: y" - 5y + 4y = 2et (

A:

Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

Q: Solve the particular differential equation, with the initial condition: y(0)=0

A: Use separable variable method

Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

A:

Q: 3. Find the particular solution to the differential equation (y + 5)(x+2) if the %3D dx solution…

A:

Q: Solve the Homogenous Differential Equation: (x² + y³) = xy ху.

A: This question is based on solution of Homogeneous differential equation.

Q: dy dx X2 (1+y2)

A: Let's solve given diffrential equation.

Q: dy dx 11 - 4xy, when x = 0, y = 2

A:

Q: Find the special solution of ele differential equation. = 20x - 4x3 dy dx y with the initial value…

A:

Q: The particular solution of the following nonhomogeneous differential equation y" – 2y' +y = x² + e¬*…

A:

Q: Find the linear homogeneous differential equation with constant coefficients and the general…

A: Given the solution is y=2+3x-4x2e4x+e4x   NOTE: If Auxiliary equation of a differential equation…

Q: 2. | Determine the general solution of the given differential equation y" -6y" = 3- cos x

A: The solution is given as

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.