MATH 2410Q Lecture 8: Substitution

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Techniques so far check guess separation of variables. Ex date fcx y substitute a new variable u for y y u g hex y gcx. us fox gcx. ie fix. In 1 1 1 c x c iy e. X e l xu y dy udxtxdu ut x du dx t udxtxdu. 9 dx u x tied x c xd u. U x cx ln y substitution u works for the dad f cx y if f is homogeneous is homogeneous if to fix y fcx y. Le fctx ty eid"t e t fcx. us to fox y homogeneous w degree of o. X so n ctx ty both degree 1. Ex ey t lx y tx so homogeneous dy d flax 1 by. En u n dd n whole eqn by u. Becomes w substitution u y h d tll n pcx u. Ext x dat y tz dat t"t y becomes. 3 11 1 3 1214 3 13x es dx fkntxt.

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