An Elementary Course in the Integral Calculus
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In our eReader you can find the full English version of the book. Read An Elementary Course in the Integral Calculus 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 An Elementary Course in the Integral Calculus
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On putting it in the ordinary form (1), it becomes dx X y^^-.-n Here P = — , and hence, the integrating factor e = e ' = e ^^S = -.
x X By using this factor, and adopting the differential form, the equation is changed into -dy ydx = xdx.
X- x^ w 1 1 Integrating, ^ = -x'^ + c, or a = -x^ + ex.
X 2 2 Ex. 2. Solve ^ + 2/ = e-«.
dx Ex. 3. Solve ^ + ^ ~^^ y = 1.
dx x^ Ex.4. Solve ^ + -i^-2/ = i -■ dx x^ + 1 (a;2 + l)3 Ex.5. Solve ^ + ^2,=^.
dx X x" 103. Equations reducible to the linear form. Someti...mes equa- tions that are not linear can be reduced to the linear form. One type of such equations is ^ + Py=Qr, dx in which P, Q, are functions of x, and n is any constant. Divi- sion by 2/" and multiplication by {—ii + 1) gives i-n + l) y-"^ +{-n + l) Py-+^ = (- n + 1) Q.
210 INTEGRAL CALCULUS [Ch. Xlll.
On substituting v for y~"^^, this reduces to ax which is linear in v.
Ex. 1. Solve ^ + iy = x'^y^.
dx X Division by y^ gives y-^ 2^ _)_ _ y-i — x^.
dx X On putting v for y^, this takes the linear form V =— ox*^.
What to read after An Elementary Course in the Integral Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Daniel a Daniel Alexander Murray to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
On putting it in the ordinary form (1), it becomes dx X y^^-.-n Here P = — , and hence, the integrating factor e = e ' = e ^^S = -.
x X By using this factor, and adopting the differential form, the equation is changed into -dy ydx = xdx.
X- x^ w 1 1 Integrating, ^ = -x'^ + c, or a = -x^ + ex.
X 2 2 Ex. 2. Solve ^ + 2/ = e-«.
dx Ex. 3. Solve ^ + ^ ~^^ y = 1.
dx x^ Ex.4. Solve ^ + -i^-2/ = i -■ dx x^ + 1 (a;2 + l)3 Ex.5. Solve ^ + ^2,=^.
dx X x" 103. Equations reducible to the linear form. Someti...mes equa- tions that are not linear can be reduced to the linear form. One type of such equations is ^ + Py=Qr, dx in which P, Q, are functions of x, and n is any constant. Divi- sion by 2/" and multiplication by {—ii + 1) gives i-n + l) y-"^ +{-n + l) Py-+^ = (- n + 1) Q.
210 INTEGRAL CALCULUS [Ch. Xlll.
On substituting v for y~"^^, this reduces to ax which is linear in v.
Ex. 1. Solve ^ + iy = x'^y^.
dx X Division by y^ gives y-^ 2^ _)_ _ y-i — x^.
dx X On putting v for y^, this takes the linear form V =— ox*^.
What to read after An Elementary Course in the Integral Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Daniel a Daniel Alexander Murray to read onlineMoreLess
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