InterviewSolution
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InterviewSolution
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Solve the differential equation `(1+x^(2))(dy)/(dx)=x`. |
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Answer» `(1+x^(2))(dy)/(dx)=x` Integrate both sides with respect to `x` `(dy)/(dx)=(x)/(1+x^(2))` Integrate both sides with respect to `x` `(dy)/(dx)*-dx=int(x)/(1+x^(2))dx+c` Let `1+x^(2)=t` `implies int dy=int(x)/(1+x^(2))+cimplies2x=(dt)/(dx)` `implies y=int(dt)/(dx)+cimpliesxdx=(dt)/(2)` `implies y=(1)/(2)logt+c` `impliesy=(1)/(2)log(1+x^(2))+c`. |
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