Which of the following statements are true for the differential equation given b

Question

Which of the following statements are true for the differential equation given below? y' = (k_1 x^2 + k_2 y^2)/(k_3 xy) The equation can be solved by the method for homogeneous differential equations for any non-zero values of constants k_1, k_2 and k_3. The equation can be solved by the method for Bernoulli equations for any non-zero values of constants k_1, k_2 and k_3. The equation can be solved by the method for exact differential equations for any non-zero values of constants k_1, k_2 and k_3 Statements 1 and 2 are true Statements 1 and 3 are true Statements 2 and 3 are true All the statements are true

Explanation / Answer

the given differential equation can be simplified

y'=(k1x^2+k2y^2)/(k3xy)=(k1/k3)*(x/y) + (k2/k3)*(y/x) this is Bernoulli equation can solve

And y'=(1+(k2/k1)*(y/x)^2)/((k3/k1)*(y/x)) this is homogeneous differential euation can solve

(c) statment 1 and 2 are true..................ans

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