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The given differential equation is $1+(\frac{d^{3}y}{dx^{3}})^{3}=\lambda\frac{d^{2}y}{dx^{2}}$. The highest order derivative present in the equation is $\frac{d^{3}y}{dx^{3}}$. Therefore, the order of the differential equation is 3.
The degree of a differential equation is defined as the highest power of the highest order derivative, provided the equation is a polynomial in terms of derivatives. Here, the highest order derivative is $\frac{d^{3}y}{dx^{3}}$, and its exponent is 3. Since the equation is already in polynomial form with respect to its derivatives, the degree is 3.
Final Answer: Order = 3, Degree = 3