(a) y = Ae + Be+Ccos 2x + Dsin 2x

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: 7. 2yy = e-: y(4) =-2

A:

Q: y + 3xy' – 2(y')³ = 0

A: Product rule of differentiation: (fg)'=fg'+gf' Chain rule of differentiation:…

Q: Find the general solution of the differential equation.

A: given,

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

A:

Q: Find the differential equation of the cubics : cy^2= x^2 ( x - a ) with a held fixed.

A: Here c is arbitrary constant and a  is fixed. So we have to find a differential equation which does…

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

A:

Q: Find general solutions of the differential equation  2xyy'=x^2+2y^2

A: To solve:

Q: III. dy y³ dx x²y-xyz

A: Sol:- y' =y3x2y-xy2Substitute y=vx, v is a function of xxv' +v=v21-vRewrite in the form of a first…

Q: find solution of differential equation y'=(x^3+3y^2)/2xy

A:

Q: Find general solutions of the differential equation  (2x+1)y'+y=(2x+1)^3/2

A: Consider the differential equation:

Q: A solution for the differential equation is y = Pe-3x/2 + Qe-x/2.

A: Here P and Q are two Arbitary constant ,so the heighest order of the differential equation is 2.

Q: The solution of the differential equation y" – 2y' = x + sinx

A: we have to solve the given differential equation

Q: Determine the solution to the differential equation given by: (2xy-9x2)dx+(2y+x2+1)dy=0

A: Here,      2xy-9x2dx+2y+x2+1dy=0⇒2xy-9x2+2y+x2+1dydx=0⇒2xy-9x2+2y+x2+1y' =0Here, ∂Mx, y∂y=∂Nx, y∂x.…

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

A: We first separate the variables

Q: II. dy dx 2x² x(y² + 1)

A: We have to find the best way to solve the given First Order Differential Equation by Finding…

Q: Solve the differential equation 1.) dy = (y²xe^3-3x²y)dx

A: Please see the below picture for detailed solution.

Q: Find general solutions of the differential equation      2x^2y-x^3y'=y^3

A: 2x2y-x3y'=y3 We need to find the general solutions of the differential equation.

Q: find the solution of this differential equation: (x − 1)y′ = y + 2(x − 1)^3

A:

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

A:

Q: How can I solve this differential equation? (x^2+1)(dy)/(dx)+y^2=-1, y(0)=1

A:

Q: Find general solutions of the differential equation       3y+x^4y'=2xy.

A: This can be solved using the standard format: dy/dx + P(x)y = Q(x)

Q: Find general solutions of the differential equation      y'=y+y^3

A:

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

A: An equation which involves the derivative or differential coefficient is called differential…

Q: *- 2- 2 - - 2 = 0 dx dx

A: The solution is given below-

Q: How do I solve this differential equation using P(x), Q(x) and v(x)?

A: The given differential equation is,

Q: y' + 2y = 2+ 3x

A:

Q: Find general solutions of the differential equation          x^3+3y-xy'=0.

A:

Q: The general solution of the differential equation 2x(y + 1) dx — у dy is:

A: Given the differential equation: Now,

Q: 2) x – 1 = - 2e-y

A:

Q: Find the general or Special Solution to the differential equation 2 y = (x-y₁²

A:

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

A:

Q: y =Cjx +Cze* %3D

A:

Q: Find general solutions of the differential equation     y'=(4x+y)^2

A:

Q: The solution of the differential equation y'+=y' is

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Find the solution of differential equation 4 dx2 +y = sin).

A: The given differential equation is 4d2ydx2+y=sinx2. Find the solution of the differential equation…

Q: The solution of the differential equation y+=y is

A: Given, y'+yx=y2

Q: (メyーx+24 -2) dx- (x+ 4x) 0

A:

Q: the general solution of the differential equation (2xy- sec2x) dx + (x  + 2y) dy = 0

A: First, find the exact form of the equation to which it belongs.

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

A:

Q: Determine the form of a particular solution for each differential equation 1. y" - 2y + y = 10e -2x…

A:

Q: Find general solutions of the differential equation    y'+3y =3x^2e^-3x

A: y'+3y=3x2e-3x Comparing with y'+Py=Q, we get P=3  &  Q=3x2e-3x Now integrating factor is,…

Q: Solve the differential equation by an appropriate method. y''+2y'=x^2+4e^2x

A: Given linear differential equations with constant coefficients. We have find General solution for…

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

A:

Q: solution to this differential equation: (x5-y2)dx + 2xy dy = 0

A: Given differential equation is x5-y2dx+2xydy=0

Q: Find general solutions of the differential equation        2xy'+y^3e^(-2x)=2xy

A: Rewrite the equation. Multiply the equation by 1/y 3 . Let 1/y 2 = t . Differentiate both sides…

Q: Find the solution of differential equation 4º+y = sin dx2

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.