4-x-y Problem 5 Solve the differential equation y'= (Hint: let u = x + y) 3x+3y

Q: 12. Solve the second-Order differential equation: d²y - y = e* (use method of variation of…

A:

Q: 1. The point (0,1) is intersect point of the differential equation (2x – 3y – 1)dx – [6(2x - 3y) –…

A: (2x-3y-1)dx-(6(2x-3y)-1)dy=0dydx=6(2x-3y)-1(2x-3y)-1 let…

Q: 5. Solve the higher order differential equation 2.xy" – y' + 2y=0.

A:

Q: 5.Find the general solution of the differential equation y'=x-y+3/x-y

A:

Q: 1. Solve the differential equation (3xy- 2y)dx + (x²- 2xy)dy = 0

A: Solve the above integration

Q: find the solution of differential equation x²y' = xy + x²ex

A:

Q: 5. Find the solution of the differential equation y =- xy + xy³ (Bernoulli)

A:

Q: ...... 19. Find the general solution of the differential equation 2x2 =x² + y² dx

A: We have to solve given problem:

Q: find the solution of differential equation y' = 1+ e*-y

A:

Q: 1. Find real-valued fundamental solutions of the differential equation 1 x' = Ax, A= 2 %3D 4 -3

A: We need to find the solutions of given differential equations. Given - X' = AX, where A = 1-24-3 So,…

Q: 1. Solve the differential equation: xy' – y = 2x In x

A: Use linear differential equation concept

Q: 1 Solve the differential equation 2 2zy' with the initial condition y (1) = 1.

A: The given differential equation is,1y2-2x=2xy'y3having the initial condition y(1)=1

Q: show that there exists a unique solution to the differential equation y'=ln(xy); y(2)=1  the…

A:

Q: 7. To solve the initial value problem 1 dy - y(x) = e *, x> 0, y(1) = 4, dx a. Write the…

A: a) Standard Form:

Q: 2. The differential equation (4x'y'-6x'y-2r-3)dr +(2x*y-2x' ty = 0 is exact because aN

A:

Q: y" +y = 1.

A:

Q: Consider the initial-value problem (x² − 1)y"+y' + y = ex y(1) = 1 y' (1) = -1 Does the Existence…

A:

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: 5. Find the general solution of the differential equation y=(2y4+2x)y'.

A: Given differentiatial equation: y = (2y^4+2x)y'  Here y'= dy/dx

Q: 2. Solve the differential equation dy -e2y-cotx tan x dx

A: On differentiating the given equation, tan2 x.dydx=e2y.e-cotxe-2ydy=e-cotxtan2x.dxLet, cotx=t…

Q: Find general solutions of the differential equation    (x^2-1)y'+(x-1)y=1

A:

Q: 1. Choose a solution to the differential equation y" - y = x²e² + 5.

A:

Q: 1. What can you say about a solution of the equation y' = 49y² just by looking at the differential…

A: Given that : y' = 49y2. This is a differential equation and we find solution of this differential…

Q: Example 7: Find the differential equation corresponding to y = ae* +be* +ce", where aA c are…

A: Answer:

Q: 11. Solve the differential equation y+y = 0 using power series.

A: In power series method is used to find a power series solution to given differential equation.

Q: > (/xy -x)dy+: ху

A:

Q: find the solution of differential equation y' = 1+e-y

A:

Q: Yp = -1 / 5ex - 1/2 (cos 2x) ((ln (sec2x + tan2x)) is the particular solution of the differential…

A: A solution yp(x) of a differential equation that contains no arbitrary constants is called a…

Q: Solve the differential equation y""+y" = 3x² + sin x - 2 cos x What is the particular solution?

A: We have to find the particular solution.

Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

A:

Q: 7) Solve the differential equation. (ev – 1)y = 2 + cos x -

A: Given: ey−1y'=2+cos⁡x ⇒ey−1dydx=2+cos⁡x ⇒ey−1dy=2+cos⁡xdx Now to solve the given differential…

Q: Example 5: Solve the given differential equation 2 = 2 y %3D dx 2.

A:

Q: 7. Solve the differential equation y' + y2sin x = 0, y(0) 1.

A: The solution is given as

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: 19. The differential equation (2xy - y^2+ y) dx + (3x^2 - 4xy + 3x) = 0 is

A:

Q: 1.. The differential equation (3x² + 2.xy + 4y²)

A:

Q: 12. Solve the second-Order differential equation: a²y dx2 -y = e* (use method of variation of…

A:

Q: EXAMPLE 2.3. Determine the differential equation that is satisfie by y(t) = c1x + c2e*

A: Topic - differential equation

Q: 1 - 5y. 3D

A:

Q: 3. The differential equation = 8 – 2y can be solved using the method of separation of variables or…

A: solve using separation of variable dydt=8-2y dydt=-2y+8 dydt=-2y-4 dyy-4=-2dt take integration…

Q: 5. A differential equation is if it can be written in the form f(y)d(y) = g(x)d(x).

A: ## Given differential equation       f(y)d(y) = g(x)d(x)

Q: 4.1 Find the general solution of second order differential equation y" + 4y = x²sin (2x)

A:

Q: 13. Solve the ivp differential equation: +y = e2x; y(0) = 0,y'(0) = dx

A:

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

A:

Q: 1. Solve given separable differential equation: y' + 2x(y² - 3y + 2) = 0

A: Let us consider the differential equation of the form  dydx=f(x)g(y) Solving the equation using the…

Q: 3. a. Solve the differential equation y'= 2x√/1-y² b. Explain why the initial value problem y'=…

A:

Q: 1. Find the general solution of the given differential equations: y/ - y = x +1

A: We have to solve the given differential equations.

Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Given xdy-y+xy3(1+lnx)dx=0

Q: 1. Solve the differential equation (3xy – 4y2)dx + (x2 – 4xy)dy = 0 -

A: Given differential equation is  (3xy-4y2)dx+(x2-4xy)dy=0 This is of the form  M(x,y)dx+N(x,y)dy=0…