InterviewSolution
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InterviewSolution
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Find the order and degree of the following differential equations. i) `(dy)/(dx)+y=1/((dy)/(dx))`, ii) `e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0` , iii) `sin^(-1)(dy)/(dx)=x+y`, iv) `log_(e)(dy)/(dx)=ax+by` v) `y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0` |
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Answer» i) `(dy)/(dx) +y=1/(dy)/(dx)` `therefore ((dy)/(dx))^(2)+y(dy)/(dx)=1` Hence order is 1 and degree is 2. ii) `e^(d^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0` Clearly order is 3, but degree is not defined as it cannot be expressed as a polynomial equation in derivatives. iii) `sin^(-1)(dy)/(dx)=x+y` `therefore (dy)/(dx)=sin(x+y)` Hence order is 1 and degree is 1. iv) `log_(e)(dy)/(dx)=ax+by` `therefore (dy)/(dx)=e^(ax+by)` Hence order is one and degree is also 1. v) `y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0` Clearly, order is 2 and degree is 1. |
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