InterviewSolution
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InterviewSolution
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Verify that`y=c e^(t a n-1_x)`is a solution of differential equation`(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=0.` |
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Answer» `y=c*e^(tan^(-1)x)` …………`(1)` Differentiate with respect to `x` `(dy)/(dx)=c*e^(tan^(-1)x)*(1)/(1+x^(2))` `implies (1+x^(2))(dy)/(dx)=c*e^(tan^(-1)x)` `implies (1+x^(2))(dy)/(dx)=y` [From eq. `(1)`] Again differentiate with respect to `x` `(1+x^(2))(d^(2)y)/(dx^(2))+(dy)/(Dx)*2x=(dy)/(dx)` `implies (1+x^(2))(d^(2)y)/(dx^(2))+(2x-1)(dy)/(dx)=0` `:. y=c*e^(tan^(-1)x)` is a solution of the given differential eqaution. |
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