## Differential equations |

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arbitrary constant auxiliary equation axis called change of variable Clairaut's equation complete equation conics coordinates and slope cuts the members derivative direction field distance dM dN double root dx dx dx dy dy dx dy/dx exact differential exact equation Example EXERCISES Find EXERCISES Solve family of curves Find the differential Find the motion force friction function given Hence homogeneous functions homogeneous of degree hyperbolas independent variable integral curve integrating factor interval lineal element linear equation linearly dependent method one-parameter family orifice origin orthogonal trajectories parabolas parameter PARTIAL DIFFERENTIAL EQUATIONS particular solution path plane problem reduced equation replace result Riccati's equation satisfy the differential second order Show singular solution solution of 2-1 straight lines substituting subtangent tangent tion ui(x vanish variables are separable velocity is proportional vibration whence Wronskian