y = C1e2" sen(x)+ C2e²" cos(x) +x² + C3x + C4.

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

A: Given the differential equation y’ = 1 – ( y – x + 1)2 and we have to show that y  = x -1 is a…

Q: find the general solution of the first-order linear differential equation. y' + (tan x)y = cos x

A:

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: Given

Q: Formulate a differential equation that is satisfied by 1. y=Ae2+ Bxe2x 2x + Bxe2x

A: The given equation is: y=Ae2x+Bxe2x Formulate a differential equation that is satisfied by the given…

Q: Find the particular solution of the first-order linear differential equation for x > 0 that…

A: Find the particular solution of the first-order linear differential equation for x > 0 that…

Q: What function satisfies the differential equation y - y' = 0?

A:

Q: Show that the differential equation  (2xy3 - 3y2 + 2xy2)dx + (3x2y2 - 6xy + 2x2y)dy = 0 is exact and…

A: To show that the differential equation  2xy3-3y2+2xy2dx+3x2y2-6xy+2x2ydy=0 is exact and to find its…

Q: Find the general solution of the differential equation. (Use C for any needed constant.) y' = 10VX y…

A:

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

A:

Q: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by undetermined coefficients…

A: To solve the following problem

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

A:

Q: Solve the Cauchy-Euler differential equation x -2x+2y = x dx dx

A:

Q: 7. Find the particular solution of the differential equation dx +5x³y x³ passing through the point

A: Given, dydx+5x3y=x3,   0,72 it is a linear differential equation p(x)=5x3,  q(x)=x3…

Q: 5. Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y )²

A: We have to evaluate: (y(x) + 1) ( d^2 y(x))/( dx^2) = (( dy(x))/( dx))^2:Treating y as the…

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

A: x2y” + 3xy’ - 3y = 0

Q: Find the particular solution of the differential equation 2xy′ − ln x2 = 0, x > 0 that satisfies…

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′ + 3y = e3x for x >…

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 particular solution that satisfies the differential equation and the initial condition. x²…

A:

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: Determine the form of a particular solution for each differential equation. y'' - 2y' + y =…

A: We have to determine the form of a particular solution for each differential equation.…

Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

A:

Q: form the differential equation corresponding to (y-b)2=4(x-a)

A: (y-b)2 = 4(x-a)

Q: Find the general solution of the differential equation 2xyy' = 2y² – x²

A: given 2xy y' = 2y' -x'y' = 2y2-x22xy---(1)put y =vxy' = v + xv'---(2)so from (!) we have y' =…

Q: y' = y + y3

A:

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: Since you have asked multiple questions, we  will solve the first question for you. If you want any…

Q: What is the general solution to the differential equation (2xy - y² + y)dx + (3x² - 4xy + 3x)dy = 0…

A: 2xy-y2+ydx+3x2-4xy+3xdy=0

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: Given that f'(x) = 20x3 - 8x and f(1) = 1 then find particular solution. Here i attached solution of…

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: 2) x – 1 = - 2e-y

A:

Q: y = Clx+ C2e

A:

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: We have given the general solution y = C1 + C2e2xcos 5x +  C3e2xsin 5x

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

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

A:

Q: Find the general solution to the non-homogeneous differential equation. y" - 3y' = sin(3x)

A:

Q: Find the general solution of the differential equation using any method         y′ = ln(x2 + x)

A: we have to find the solution of the given differential equation  y′ = ln(x2 + x)

Q: Determine the form of a particular solution of the differential equation y" + 9y = e*cos3x + x² +…

A:

Q: Find the solution to the first order differential equation using any acceptable method.…

A: Given: The first order differential equation is (y2+1)dx = (ysec2x)dy.The initial condition is…

Q: obtain the linear differential equation with the real, constant coefficients that is satisfied by…

A: Solution.

Q: y' = ycotx + y²cscx

A:

Q: Find general solutions of the differential equation  (x^2-y^2)y'=2xy

A:

Q: Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y ')²

A: Let y' = t Then , y''=dtdy  to find the value of y, integrate y' =t⇒∫dy =∫t. dt⇒      y =t22  So the…

Q: Solve Bernoulli's Equation y(2xy+e )dx-e'dy 0 to reduce into Linear 01 Form of Differential…

A: As per bartleby expert policy only one individual question is to be answered. Kindly repost…