Using variable separable find the complete solution of the given differential equations xy3dx+(y+1)e−xdy

zagonek34

zagonek34

Answered

2021-12-27

Using variable separable find the complete solution of the given differential equations
xy3dx+(y+1)exdy

Answer & Explanation

Maria Lopez

Maria Lopez

Expert

2021-12-28Added 32 answers

xy3dx+(y+1)exdy=0
xy3dx=(y+1)exdy
xdxex=(y+1)y3dy
xexdx=yy31y3dy
xexdx=y2y3dy
Integrate on both sides
xexdx=y2y3dy
xexex=y2+12+1y3+13+1+c
xexex=1y+12y2+c
Travis Hicks

Travis Hicks

Expert

2021-12-29Added 29 answers

Step 1
The given equation is:
xy3dx+(y+1)exdy=0
We can rewrite this as:
xy3dx=(y+1)exdy
Divide both sides by exy3
xexdx=(y+1)y3dy
This is variable separable form
Step 2
We can solve the equation by integrating equation we have got in Step 1
xexdx=(y+1)y3dy
xexex.1dx=(y2+y3)dy
xexex=y2+12+1y3+13+1+C
ex(x1)=1y+12y2+C
ex(x1)=2y+12y2+C
Step 3
Answer: ex(x1)=2y+12y2+C
karton

karton

Expert

2022-01-10Added 439 answers

xy3dx+(y+1)exdy=0xy3dx=(y+1)exdyxdxex=(y+1)y3dyxexdx=yy31y3dyxexdx=y2y3dyxexdx=y2y3dyxexex=1y+12y2+c

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