The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and solve the equation by using the substitution u = y'. x2y" + (y')² = 0 y(x) = ||

Q: Find the general solution of the given differential equation and use it to determine how solutions…

A:

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

A:

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

A: Given that        y''+y'2+4=0‐‐‐‐1        we have to solve this using the substitution        u=y'

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: Assume that the rate of change of y is proportional to y. Solve the resulting differential equation…

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

A:

Q: What is the particular solution to the differential equation with the initial dx condition y(-2) =…

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

A:

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

A: To Determine: Find the general solution of the first-order differential equation by any appropriate…

Q: The equation x² + e¤y = c defines an implicit solution of the differential equation

A: We have to differentiate the given equation with respect to x first.

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: Find the solution for the second order differential equation y-4y = x sinh x.

A:

Q: 2. y-폼-y 1 ミ、 6x 3x2 ||

A:

Q: The solution of the ordinary differential equation y" – y" = 0 is:

A: The given ordinary differential equation is:y'''-y''=0The auxiliary equation is:D3-D2=0

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

A:

Q: What is the general solution of the differential equation; y’ = 2x cos (x^2)

A: solution:-y'=2x cosx2solving the differential equation we getdydx=2x cosx2y=∫2x cosx2 dxlet x2=t2x…

Q: Find the general solution of the given differential equation 1 2 -y' + y = -x(secx)²y2 x2

A:

Q: Find the general solution of the given differential equation y" + y = 0

A:

Q: y(4) – 16y" = e¯* + sin3x y

A: find complementary function and particular integral and add them

Q: y = c1 e(-2+v3)x + c» + c2 e(-2-v/3) z

A:

Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

A:

Q: Solve the differential equation with initial conditions y" - 3y 10y = 4e5t y(0) = 0, y' (0) = 1…

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: If we use the method of variation of parameters, the particular solution of the following…

A:

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

A:

Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

A:

Q: Write down a linear homogenous differential equation (with the smallest order and constant…

A:

Q: Solve the given differential equation by separation of variables. y In(x) *- (1)* %3D Ap

A: Solution :-

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: 2. Solve the first order linear differential equation y'+2xy = x, with initial value y(0) =1.

A:

Q: The dependent variable y is missing in the given differential equation. Solve the equation by the…

A:

Q: The solution of the following homogenous differential equation y' = - x+y -is

A: We find the solution of the homogeneous differential equation y'=yx+y

Q: The complementary solution for following differential equation d3x + 5 d2x +26 dt2 dx dt3 150х 600t…

A: In the question it is asked to calculate the complementary solution of the function given below.…

Q: Solve the 2nd order linear differential equation y" + y' +10y =

A:

Q: 1. x²y y' = ey

A: Lambert W Function: The general solution of any equation of the form xex = a is given by the…

Q: Find the differential. Equation by eliminating the arbitrary constant  y = Ae2x + Be-2x

A:

Q: yV + 16y = 0

A:

Q: Find the general solution of differential equation, and when initial conditios are given, the…

A:

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: Show that given differential equation is not exact and hence find its general solution (x³ + y°)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.