Differential Equations
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In our eReader you can find the full English version of the book. Read Differential Equations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Differential Equations
What reading level is Differential Equations book?
To quickly assess the difficulty of the text, read a short excerpt:
Example 2. (1 + 'jp) dx — {xy -\- y -\- rf) dy = 0.
This is an equation of the first degree in x and dx.
Dividing by (1 + y') dy, it becomes dx y _ d^'TTJ'"^'^' P is here a function of y and fPdy J e = , multiplying by this factor, the equation becomes dx xy dy _ y dy whence and x = l + y^ + c VlTW- 14. Equations Reducible to Linear Form. — An equation of the form ^ + Py = Qy" (14) where P and Q are functions of x can be made Unear by a change of variable. Dividing by y^it becomes y^f^ + Py--+'... = Q.
24 DIFFERENTIAL EQUATIONS Chap. II If we take 2/'~" = u as new variable the equation becomes 1 du 1 — ndx which is Knear.
Example. -^ + -y = ^- ax X 3?
+ Pu = Q, Division by y^ gives Let Then -sdy ,2 _2 ^ 1^ ^ dx^x^ a?' u = y-^.
whence £ = -^^l"' ^ dx 2dx Substituting tnese values we get and so Idu 2 ^1^ 2dx X cc' du 4 dx X : This is a linear equation with solution 1 3x^ w = qV2 + ^' or, since u = y~', Chap. II OTHER FIRST ORDER EQUATIONS 25 15. Homogeneous Equations. — A function / (x, y) is said to be a homogeneous equation of the nth degree if J{tx,ty) = t»fix,y).
What to read after Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by H B Henry Bayard Phillips to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Example 2. (1 + 'jp) dx — {xy -\- y -\- rf) dy = 0.
This is an equation of the first degree in x and dx.
Dividing by (1 + y') dy, it becomes dx y _ d^'TTJ'"^'^' P is here a function of y and fPdy J e = , multiplying by this factor, the equation becomes dx xy dy _ y dy whence and x = l + y^ + c VlTW- 14. Equations Reducible to Linear Form. — An equation of the form ^ + Py = Qy" (14) where P and Q are functions of x can be made Unear by a change of variable. Dividing by y^it becomes y^f^ + Py--+'... = Q.
24 DIFFERENTIAL EQUATIONS Chap. II If we take 2/'~" = u as new variable the equation becomes 1 du 1 — ndx which is Knear.
Example. -^ + -y = ^- ax X 3?
+ Pu = Q, Division by y^ gives Let Then -sdy ,2 _2 ^ 1^ ^ dx^x^ a?' u = y-^.
whence £ = -^^l"' ^ dx 2dx Substituting tnese values we get and so Idu 2 ^1^ 2dx X cc' du 4 dx X : This is a linear equation with solution 1 3x^ w = qV2 + ^' or, since u = y~', Chap. II OTHER FIRST ORDER EQUATIONS 25 15. Homogeneous Equations. — A function / (x, y) is said to be a homogeneous equation of the nth degree if J{tx,ty) = t»fix,y).
What to read after Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by H B Henry Bayard Phillips to read onlineMoreLess
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