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Differential Equations of First Order and First Degree
Linear Differential Equations with Constant Coefficients
6 other sections not shown
arbitrary constants assume beam c-discriminant called Chapter characteristic equation circuit Clairaut's equation coefficients convergence deflection curve dependent variable derivatives determine differential equation dx/dt dy/dx envelope equa equal to zero equation becomes equation of motion Euler's formula exact differential EXAMPLE EXERCISE existence theorem family of curves Find the orthogonal frequency ft./sec function given gives Hence homogeneous equation initial conditions integral curves integrating factor limiting velocity linear equation mass Newton's Second Law obtain one-parameter family original equation orthogonal trajectories particular integral particular solution poundals pounds recursion formula Replacing resistance roots Separating variables Show singular point singular solutions sinh slope Solve the equation spring student substitution tangent tank temperature tion transformation values vertical weight write x-axis x)dy y)dx y)dy