Show transcribed image text dy dr Solution: We can write the equation as to get both homogeneous of degree 2. Thas, the DE is homogeneous So, let tur, so 훑-t, + r -|and-t. Ststituting in gives de 2 3 dx 2 de 2+4 dr 2 thas 2e and so Note: Alternatively, you could use an appropriate integrating factor to transform the given equation into an exact equation and then solve this exact equation by the usual method: Multiplying both sides of the DE by μ results in an exact DE: Which you can then solve (to get the same answer as above). Note 2: The given DE can also be seen to be a Bernoulli-type equation (with n–1) and can be solved as such.
dy dr Solution: We can write the equation as to get both homogeneous of degree 2. Thas, the DE is homogeneous So, let tur, so 훑-t, + r -|and-t. Ststituting in gives de 2 3 dx 2 de 2+4 dr 2 thas 2e and so Note: Alternatively, you could use an appropriate integrating factor to transform the given equation into an exact equation and then solve this exact equation by the usual method: Multiplying both sides of the DE by μ results in an exact DE: Which you can then solve (to get the same answer as above). Note 2: The given DE can also be seen to be a Bernoulli-type equation (with n–1) and can be solved as such.
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