Find the order and degree (if defined) of the differential equation $$\dfrac{d^{2}y}{dx^{2}}+x\left(\dfrac{dy}{dx}\right)^{2}=2x^{2}\log\left(\dfrac{d^{2}y}{dx^{2}}\right).$$

CBSE Class 12 · 2019 · Differential EquationsVery Short Answer

Find the order and degree (if defined) of the differential equation

\frac{d ^{2} y}{d x ^{2}} + x (\frac{d y}{d x})^{2} = 2 x^{2} lo g (\frac{d ^{2} y}{d x ^{2}}) .

Answer: Order $= 2$ ; degree is not defined

The highest-order derivative is

\frac{d ^{2} y}{d x ^{2}}

, so the order is

2

.
Because

\frac{d ^{2} y}{d x ^{2}}

appears inside a

lo g

, the equation is not a polynomial in the derivatives.

Order = 2, degree is not defined

CBSE Class 12 Board · 2019 · Subjective