InterviewSolution
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InterviewSolution
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If `y^2=a x^2+b x+c`, then `y^3(d^2y)/(dx^2)`is(a) a constant (b) a function of `x`only(c) a function of `y`only (d) a function of `x`and `y`A. a constantB. a function of x onlyC. a function of y onlyD. a function of x and y |
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Answer» `y^(2)=ax^(2)+bx+c` `"or "2y(dy)/(dx)=2ax+b` `"or "2((dy)/(dx))^(2)+2y(d^(2)y)/(dx^(2))=2a` `"or "y(d^(2)y)/dx^(2)=a-((dy)/(dx))^(2)` `=a-((2ax+b)/2y)^(2)` `=(4ay^(2)-(2ax+b)^(2))/(4y^(2))` `"or "4y^(3)(d^(2)y)/(dx^(2))=4a(ax^(2)+bx+c)-(4a^(2)x^(2)+4bax+b^(2))` `"or "4y^(3)(d^(2)y)/(dx^(2))=4ac-b^(2)= constant` |
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