Solve the ff Differential equations. Indicate the type of differential

socorraob

socorraob

Answered question

2021-12-20

Solve the ff Differential equations. Indicate the type of differential equation
ylnxlnydx+dy=0

Answer & Explanation

braodagxj

braodagxj

Beginner2021-12-21Added 38 answers

Step 1
Given: y(lnx)(lny)dx+dy=0
(lnx)dx=dyy(lny)
The above differential equation is of variable separation form.
Step 2
Integrating both sides, we get
lnx dx=dyylny
Let lny=t1ydy=dt
Using integration by parts
(lnx)1dx(ddx(lnx)1dx)dx=lnt+c
(lnx)x1xx dx=lnt+c
(lnx)x1dx=lnt+c
xlnxx=ln(lny)+c
Pademagk71

Pademagk71

Beginner2021-12-22Added 34 answers

ylnylnxdx+dy=0
dyylny=lnxdx
Integrate dyylny=lnxdx
lnxdx=xlnxx(1x)dx=xlnxxlnC
ln(|lny|)=xlnx+x+lnC
lny=C(exxlnx)
y=eC(exxlnx)
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

dy/dx=y in xin y(y in x in y)dx+dy=0(y in xin y)dx=dy(in x)dx=(1/y in y)dy
you just need to integrate both sides

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