Ppt of first order differenatiol equation
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This document discusses differential equations and related concepts. It defines a differential equation as an equation containing derivatives of dependent variables with respect to independent variables. A first order differential equation contains derivatives of degree one. The document also discusses orthogonal trajectories, solving differential equations for orthogonal curves, and provides an example of finding orthogonal trajectories given stream lines. Additionally, it mentions Newton's second law relating force and momentum, Kirchhoff's voltage law, and initial value problems for differential equations.
Ppt of first order differenatiol equation
- 2. WHAT IS DIFFERENTIAL EQUATION? An equation contain the derivatives of one or more dependent variables, with respect to one of more independent variables, said to be differential equation WHAT IS FIRST ORDER DIFFERETIAL EQUATION? An equation of 1st degree only in respect to the dependent variables and its derivatives
- 5. AN CURVE CUTS ANOTHER CURVE AT RIGHT ANGLE THEN TWO CURVES SAID TO BE ORTHONOGLY TO EACH OTHER
- 6. STEPS TO SLOVE ORTHOGONAL TRAJECTORIES OF THE FAMILY OF CURVES F(x, y, c) = 0 or F(r, ø, c) = 0 SOLVE DIFFERENTIAL EQUATION OF THE ORTHOGONAL TRAJECTORIES F(x, y, dy/dx) or F(r, ø, dr/dø) REPLAYES THIS DIFFERENTIAL EQUATION dy/dx BY –dx/dy or dr/dø = -r2 dø/dr ( so product of slope at each point is -1) FORM DIFFERENTIAL EQUATION IN FORM F(x, y, dy/dx) = 0 or F(r, ø, dr/dø) = 0
- 7. Example : If stream lines of a flow around a corner are x y = constant find their orthogonal trajectories As by steps Differential equation of curve is x . dy/dx + y = 0 Replays dy/dx by -dx/dy Finally we get x . dx – y dy = 0 Therefore X2 - Y2 = c2 is required orthogonal trajectories
- 8. dx/dt
- 9. NEWTON’S SECOND LAW THE RATE OF CHANGE IN MOMENTUM ENCOUNTERED BY A MOVING OBJECT IS EQUAL TO THE NET FORCE APPLIED TO IT. IN MATHEMATICAL TERMS, Since m is constant then dm/dt is
- 10. Kirchhoff's law , sum of voltage drop across R and L = E
- 11. WHEN COMPARE TO I.F IS MULITIPLING I.F BOTH SIDES When ‘t=0’ then ‘i=0’ we get c = - E/R