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

Name: Using variable separable find the complete solution of the given differential equations xy3dx+(y+1)e−xdy
Uploaded: 2022-02-23T17:22:57+00:00
Description: Using variable separable find the complete solution of the given differential equations xy3dx+(y+1)e−xdy

Question

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

Maria Lopez · Accepted Answer

xy3dx+(y+1)e−xdy=0  xy3dx=−(y+1)e−xdy  xdxe−x=−(y+1)y3dy  xexdx=−yy3−1y3dy  xexdx=−y−2−y−3dy  Integrate on both sides  ∫xexdx=∫−y−2−y−3dy  xex−ex=−y−2+1−2+1−y−3+1−3+1+c  xex−ex=1y+12y2+c

Travis Hicks · Accepted Answer

Step 1   The given equation is:   xy3dx+(y+1)e−xdy=0   We can rewrite this as:   xy3dx=−(y+1)e−xdy   Divide both sides by e−xy3   ⇒xexdx=−(y+1)y−3dy   This is variable separable form   Step 2   We can solve the equation by integrating equation we have got in Step 1  ⇒∫xexdx=∫−(y+1)y−3dy  ⇒xex−∫ex.1dx=−∫(y−2+y−3)dy  ⇒xex−ex=−y−2+1−2+1−y−3+1−3+1+C  ⇒ex(x−1)=1y+12y2+C  ⇒ex(x−1)=2y+12y2+C  Step 3  Answer: ex(x−1)=2y+12y2+C

karton · Accepted Answer

xy3dx+(y+1)e−xdy=0xy3dx=−(y+1)e−xdyxdxe−x=−(y+1)y3dyxexdx=−yy3−1y3dyxexdx=−y−2−y−3dy∫xexdx=∫−y−2−y−3dyxex−ex=1y+12y2+c