Find the solution of the differential equation4xy y' = y² + x², satisfying the initial condition y(1) = 1

Q: Solve the differential equation y' = x(y – 3) with initial condition y(0) = 1.

A: Solution :-

Q: ху xy' = y(1+ln2)

A: The given differential equation is  xdydx=y1+lnyx

Q: solve the first order of differential equation dy/dx = y2 -4 using seperable method

A:

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

A:

Q: Find the general solution of the first-order linear differential equation. xy' + y = x³3 + 1

A:

Q: Solve the differential equation x y' = In x-3xy with initial-value y(1) =2.

A:

Q: find the general solution of the first-order linear differential equation. y' − (ln x)y = xx

A:

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

A:

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

A:

Q: Obtain the solution of the differential equation y′ = (x + y)^2

A: Given differential equation is: dydx=(x+y)2                       (1) Let us assume (x+y)=t…

Q: Find the particular solution of the first-order linear differential equation    y′ + (2x − 1)y = 0…

A: the given differential equation is y'+(2x-1)y=0. y(1)=2

Q: Find the ordinary differential equation from the general solution: y = Ae-* + Be-*

A: Since you have posted multiple questions and we can answer one question. So, answered first…

Q: xy"+y'=0; y1=ln(x) How can this second-order differential equation be solved by general solution?

A:

Q: (c) y' – y = e2=

A:

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

A:

Q: (c) y' – y = e2¤

A: We have to solve

Q: Find the general solution of the first-order linear differential equation y′ − y = 10

A:

Q: Determine the solution for the differential equation ry = In(x) for which Y(1)

A: y^2 = (ln x)^2  + 2 ln C

Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: The given differential equation is, y''+2y'-8y=5e-2x-e-x. Obtain the homogeneous solution.…

Q: Find the general solution of the given higher-order differential equation. у" - 2у" — Зy' — 0 y(x) =

A:

Q: y' = (4x + y)²

A:

Q: Find the differential equation by eliminating the arbitrary constant  x2-y2= 0

A: To find the differential equation x²-y²=0

Q: y(4) – 16y" = e¯* + sin3x y

A: find complementary function and particular integral and add them

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

A:

Q: Find the general solution of the differential equation: y" – 2y - 3y= - 3te. Fi: of the…

A:

Q: निर्न Cx-3)e

A:

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

A:

Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''+y=2x

A:

Q: The particular solution of the differential equation: et y" – 2y' + y =

A: Please see the explanation below

Q: 1/x+ y+(3y² + x)y =0

A: Given differential equation is of the form,  M dx + N dy=0

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

A:

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

A:

Q: y" - y = xe*, y(0) = 2, y'(0) = 1

A:

Q: Use the initial condition to find the particular solution of the differential equation. differential…

A:

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

A: Use separable variable method

Q: y = ry' – In (y')

A:

Q: Find the general solution of the first-order linear differential equation y′ + 3x2y = 6x2 for x >…

A: Given: The first-order linear differential equation: y'+3x2y=6x2 for x>0.

Q: Find general solutions of the differential equation    (x+y)y'=1

A:

Q: Find the general solution of the given higher-order differential equation. у" - 5у" - бу"%3D о y(x)

A:

Q: The differential equation: y²x + y² = x²yy' is solved by

A:

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

A:

Q: Solve the differential equation for y= y(x) if y+2ry + 2x = 2 + 2y given the initial condition that

A:

Q: Solve the initial value differential equation with initial values y(0)=2 and y'(0)=6 y" - 3y + 2y =6

A: We have to solve the given differential equation.

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

A:

Q: Solve the second order linear differential equation using method of undetermined coefficients…

A: To solve: The second order linear differential equation, 3y''+2y'-y=x2+1 using method of…

Q: The solution of the exact differential equation (ycosx + 2xe") + (sinx + x²ev – 1)y' = 0 is:

A:

Q: Find the general solution of the given second-order differential equation. 5y" + y = 0

A: To solve the given differential equation.

Q: Find the particular solution of the first-order linear differential equation    y′ − (3/x)y = 2x3…

A: Given differential equation is: y'-3xy=2x3 .................. (1) The above equation is linear in y.…