InterviewSolution
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InterviewSolution
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Find the order and degree (if any) of each of the differential equations given below:{:((i)(dy)/(dx)-tanx=0,(ii)((dy)/(dx))^(2)+y=e^(x)),((iii)(d^(2)y)=sin3x+cos3x,(iv)(y")^(2)+cosy'=0),((v)y+2y'+siny=0,(vi)(d^(4)y)/(dx^(4))+sin ((d^(3)y)/(dx^(3)))=0),((vii)y''+y^(2)+e^(y')=0,(viii)3(d^(2)y)/(dx^(2))+5((dy)/(dx))^(2)=log x):} |
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Answer» Solution :(i) The given equation is `(dy)/(dx)-tanx=0.` In the this equation, the highest-order derivative is `(dy)/(dx)` whose power is 1. `therefore` its order = 1 and degree =1. (ii) The given equation is `((dy)/(dx))^(2)+y=e^(X).` In this equation, the highest-order derivative is `(dy)/(dx)` whose power is 2. `therefore` its order =1 and degree =2. (III) The given equation is `(d^(2)y)/(dx^(2))=sin3x+cos3x.` In this equation, the highest-order derivative is `(d^(2)y)/(dx^(2))` and its power is 1. `therefore` its order = 2 and degree =1. (iv) The given equation is `((d^(2)y)/(dx^(2)))+cos((dy)/(dx))=0.` In this equation, the highest-order dervative is `(d^(2)y)/(dx^(2)),` so its order is 2. It has a term cos `((dy)/(dx)),` so its degree is not DEFINED. (v) The given equation is `(d^(2)y)/(dx^(2))+2(dy)/(dx)+siny=0.` In this equation, the highest-order derivative is `(d^(2)y)/(dx^(2))` and its power is 1. `therefore` its order = 2 and degree =1. (vi) The given equation is `(d^(4)y)/(dx^(4))+sin((d^(3)y)/(dx^(3)))=0.` In this equation, the highest-order derivative is `(d^(4)y)/(dx^(4)),` so its order is 4. It has a term `sin((d^(3)y)/(dx^(3))),` so its degree is not defined. (vii) The given equation is `(d^(3)y)/(dx^(3))+y^(2)+e^((dy//dx))=0.` In this equation, the highest-order derivative is `(d^(3)y)/(dx^(3)),` so its order is 3. (viii) The given equation is `3(d^(2)y)/(dx^(2))+5((dy)/(dx))^(2)=logx.` In this equation, the highest-order derivative is `(d^(2)y)/(dx^(2))` and its power is 1. `therefore` its order =2 and degree =1. |
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