Solve the given initial-value problem: dy/dx =(y2 − 1)/(x2 − 1), y(2) = 2

Q: Find the general solution of the differential equation dy/dx = 2.

A: dy/dx = 2 Integrate both sides w.r.t x to get: y = 2x + C where C is the constant of integration

Q: Find the general solution of the differential equation.

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Solve the initial value problem.

A:

Q: Solve the differential equation d'y dy +4 = e-3x %3D dx dx by using the method of variation of…

A:

Q: Solve the differential equation. dy 3x2y2 dx for y + 0

A:

Q: Solve the given differential equation by separation of variables. dy=x√√1-y² dx

A:

Q: Find the general solution of the differential equation y′ − ey sin x = 0

A:

Q: Solve the initial value problem dy/dx=2/x+1, y(0)=2.

A:

Q: solve the differential equation dy/dx=2x^4sqrt of y, y.0

A: Solution of given question is written in below steps.

Q: Find a general solution of the differential equation dy/dx = y2. 29.

A:

Q: Solve the differential equation dy/dx =x/y2 with initial condition y(0) = 2.

A: Given : dydx = xy2

Q: Find the complete solution of the differential equation dy dy +3 dx - 5y = e-2X sin2x dx?

A:

Q: Find the general solution to the differential equation dy/dx=x^2/y+3.

A:

Q: dy sin(t) + 1 dt

A:

Q: Solve the initial value problem. dy -=x°(y- 3), y(0) = 8 dx

A:

Q: Solve the initial value problem. dy + 3y – e -* = 0, y(0) = dx 2

A:

Q: Solve the initial value problem. √y dx + (x-4)dy=0, y(5)= 36

A:

Q: Solve the initial value problem dy + X, x > 0; y(2) = 0 x3 dx

A:

Q: Solve the initial value problems dy/dx = 10 - x, y(0) = -1

A:

Q: Find the solution of the differential equation that satisfies the given initial condition. dy 7xey,…

A:

Q: Solve the initial value problem (dx/dt)+2x=cos(4t) with x(0)=−2. x(t)=?

A: Solve the initial value problem

Q: Find an explicit solution of the given initial-value problem. dy = y sin x? , y(-2) = ; dx

A: The given equation is: dydx=y2sinx2, y-2=13

Q: Find the general solution of the differential equation dy/dx = y + 3

A: Given differential equation is dydx=y+3 Given differential can be written as: dyy+3=dx Integrating…

Q: Find the solution of the differential equation that satisfies the given initial condition dy/dx =…

A: Given, dydx=5xey y=0 when x=0

Q: Find the general solution of the differential equation dy/dx = (6 − x2)/2y3

A: dydx=6-x22y3

Q: Find the general solution of the differential equation dy/dx = 6 − y

A:

Q: Solve the differential equation dy xy y(0) = -3. dx V1+ x? There is no need to isolate y.

A:

Q: Solve the initial value problem √y dx + (x - 2)dy = 0, y(3) = 9

A:

Q: Solve the differential equation. dy = 5x dx Vy for y + 0

A: The solution are next step..

Q: Solve the given initial value problem by using the method of exactness.  xy dx+(2x2+3y2-20)dy=0,…

A: First identify M and N and check that the differential equation is exact.

Q: Find the general solution for the differential equation dy/dx=y2(1+ex)

A: the given differential equation is: we have to find the general solution for the given differential…

Q: Solve the differential equation with the given initial value condition: dy/dx = xy + 2x ; y(0) =

A:

Q: Solve the initial value problem. dy 1. dx y = xex, y(0) = e + 1

A:

Q: Solve the initial value problem dy/dx=x2−1, y(3)=7.

A: Given:

Q: Find the general solution of the differential equation dy/dx = x + 3

A: the differential equation given to us is  dydx=x+3 we will use variable separable in which dx  will…

Q: Solve the differential equation dy dx 3y3 1 %3D By the method of separating the variables

A:

Q: Find the general solution of the differential equation dy/dx = x/(x2 + 2)

A: Given: dydx=xx2+2 for finding solution of given differential equation, we use variable separable…

Q: Solve the differential equation. dy/dx = 3x2y2 for y ≠ 0

A: This question can be solved by seperating x and y terms and doing integration.

Q: Solve the given initial-value problem. dx y = 5y², x(9) = 1 dy

A:

Q: Solve the initial value problem given below. dy - 3y (-2 – y) dx

A: To Determine: solve the initial value problem.

Q: dx 10х — х2, x(0) dt

A:

Q: Solve the initial value problem: (e + y) dx + (2 +x + ye") dy = 0, y(0) = 1

A: We have to solve the initial value problem…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy = X,…

A:

Q: dy 6. Solve the initial value problem y(0) = –2. %3D - dx

A:

Q: Solve the initial-value problem dy + dx 2 e* + 1 \x – 1/ (х — 1)2 y(0) = 2

A: Given: dydx+2x−1y=ex+1(x−1)2

Q: (х5 +3у)dx — хdy —D 0

A:

Q: =e*", y(0)=1. dx Find the solution of the initial value problem

A:

Q: Find the general solution of the differential equation dy/dx = 5x/y

A: To find the general solution of the differential equation.

Q: Solve the initial-value problem for y as a function of x. (x^2+36)dy/dx=1,y(6)=0

A:

Q: Solve the initial value problem dy/dx=(x+y+1)2-(x+y-1)2  where y(0)=1/2

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.