InterviewSolution
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InterviewSolution
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If f (x) and g (x) are two solutions of the differential equation `(a(d^2y)/(dx^2)+x^2(dy)/(dx)+y=e^x, then `f(x)-g(x)` is the solution ofA. `a^(2)(d^(2)y)/(dx^(2))+(dy)/(dx)+y=e^(x)`B. `a^(2)(d^(2)y)/(dx^(2))+y=e^(x)`C. `a(d^(2)y)/(dx^(2))+y=e^(x)`D. `a(d^(2)y)/(dx^(2))+x^(2)(dy)/(dx)+y=0` |
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Answer» Correct Answer - D It is given that f(x) and g(x) are solutions of the differential equation `a(d^(2)y)/(dx^(@))+x^(2)(dy)/(dx)+y=e^(x)` `therefore" "a(d^(2))/(dx^(2)){f(x)}+x^(2)(d)/(dx){f(x)}+f(x)=e^(x)` and, `(d^(2))/(dx^(2)){g(x)}+x^(2)(d)/(dx){g(x)}+g(x)e^(x)` `rArra(d^(2))/(dx^(2)){f(x)-g(x)}+x^(2)(d)/(dx){f(x)-g(x)}+{f(x)-g(x)}=0` `rArr" "f(x)-g(x)` is a solution of the differential equation `a(d^(2)y)/(dx^(2))+x^(2)(dy)/(dx)+y=0` |
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