Solve the following differential equation by using linear equations. dx/dt = 1- t + x - tx

Bergen

Bergen

Answered question

2021-05-07

Solve the following differential equation by using linear equations.
dx/dt=1t+xtx

Answer & Explanation

Neelam Wainwright

Neelam Wainwright

Skilled2021-05-08Added 102 answers

Step 1
The given differential equation is,
dxdt=1t+xtx
For solving the given differential equation using linear equation, first we separate the terms.
dxdt=1t+xtx
dxdt=(1+x)t(1+x)
dxdt=(1+x)(1t)
dx(1+x)=(1t)dt
Step 2
Applying integration, on both the sides, we get
1(1+x)dx=(1t)dt
ln(1+x)=tt22+C
1+x=e(tt22+C)
x=e(tt22+C)1
Therefore, the general solution of the given differential equation is x=e(tt22+C)1
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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