Show that function y_{1}=x-1 is a special solution of the differential eq

preprekomW

preprekomW

Answered question

2021-09-23

Show that function y1=x1 is a special solution of the differential equation y=1(yx+1)2 and find the general solution to the equation.

Answer & Explanation

komunidadO

komunidadO

Skilled2021-09-24Added 86 answers

Step 1
Given the differential equation y=1(yx+1)2 and we have to show that y = x -1 is a solution of this differential equation also find the general solution.
Step 2
If y = x -1 is a solution of the differential equation then it satisfies the given differential equation.
y=x1y=1
Now, y=1(yx+1)2
1=1(x1x+1)2
1=1-(0)
1=1
Hence y = x -1 is a special solution of the differential equation.
Step 3
For a general solution, the differential equation is
y=1(yx+1)2
dydx=1(yx+1)2
Put yx+1=udydx1+0=dudxdydx=dudx+1
Now, put the values in DE, we get
dudx+1=1u2
dudx=u2
1u2du=dx
(1u)=x+c1u=x+cu=1x+c
Put the value of u,
yx+1=1x+c
y=x1+1x+c
Hence this is the general solution for the given differential equation.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-27Added 2605 answers

Answer is given below (on video)

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