A Short Course on Differential Equations

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Macmillan, 1906 - Differential equations - 123 pages
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Page 59 - E is the modulus of elasticity, / is the moment of inertia of a cross section of the beam about a gravity axis in the section perpendicular to the applied forces, and I is the length of the beam.
Page 75 - T r where r is the distance of the point from the center of the sphere.
Page 79 - Sx' dy and 8z' respectively. Conversely, however, an equation of the form Pdx + Qdy + Rdz = 0 where P, Q and R are functions of x, y and z, does not necessarily give rise to a solution of the form ф(ж, у, г) = с.
Page 22 - Mdx + Ndy = 0 where M and N are functions of x and y and do not contain derivatives.
Page 85 - This is a linear differential equation of the second order with constant coefficients and right hand member zero.
Page 65 - ... 0, and D = d/dx. It is readily recognized from the fact that the powers of x and of D in any term of the operator are the same. Euler's equation may always be transformed into a linear equation with constant coefficients by changing the independent variable from x to z by the substitution x = tf, or z = Inz.
Page 53 - The result when the operator is applied to the sum of a number of functions is equal to the sum of the results found when the operator is applied to each of the functions separately.
Page 7 - ORDER AND DEGREE OF A DIFFERENTIAL EQUATION The order of a differential equation is the order of the highest differential co-efficient present in the equation. Consider f) i -f> / j fi*. f* ft** f* j 2
Page 36 - Determine the curve in which the polar subnormal is proportional to the sine of the vectorial angle.
Page 26 - Ndy=Q where M and N are functions of x and y, is said to be exact when there is a function u(x, y) such that du = Mdx + Ndy. EXAMPLE. The equation Ixydx -+- afdy = 0 is said to be exact because и = хгу is such that du = 2xydx -\- x'dy.

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