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Differentiate the function with respect to x. Answer is B. I need the step. Thank you

Differentiate the function with respect to x. Answer is B. I need the step. Thank-example-1
User Kvista
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1 Answer

6 votes

Answer:

y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.

Explanation:

Rewrite the equation to -((6 c^2 - 20 x^3) dx)/(3 + 5 x^2) + dy = 0 and solve

Solve (dy(x))/(dx) = (6 c^2 - 20 x^3)/(5 x^2 + 3):

Integrate both sides with respect to x:

Answer: y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.

User Ivy Growing
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