Question

The degree of differention equation (d3y/dx3)2+2d2y/dx2−dydx+x2(dy/dx)3=0 is _________

Answer 1

Answer on Question #69661 – Math – Differential Equations

QUESTION

The degree of differential equation

$$\left(\frac {d ^ {3} y}{d x ^ {3}}\right) ^ {2} + 2 \frac {d ^ {2} y}{d x ^ {2}} - \frac {d y}{d x} + x ^ {2} \left(\frac {d y}{d x}\right) ^ {3} = 0$$

SOLUTION

By the definition,

the degree of a differential equation is the power of its highest derivative, after the equation has been made rational and integral in all of its derivatives.

(https://en.wikipedia.org/wiki/Degree_of_a_differential_equation)

We can see the equation

$$\left(\frac {\frac {d ^ {3} y}{d x ^ {3}}}{\text {highest derivative}}\right) ^ {\boxed {2}} + 2 \frac {d ^ {2} y}{d x ^ {2}} - \frac {d y}{d x} + x ^ {2} \left(\frac {d y}{d x}\right) ^ {3} = 0$$

is a polynomial equation in $y'''(x), y''(x)$ and $y'(x)$. The degree of this differential equation can be defined.

According to the above definition, the degree of the equation is 2.

ANSWER

The degree of the differential equation

$$\left(\frac {d ^ {3} y}{d x ^ {3}}\right) ^ {2} + 2 \frac {d ^ {2} y}{d x ^ {2}} - \frac {d y}{d x} + x ^ {2} \left(\frac {d y}{d x}\right) ^ {3} = 0$$

is 2.

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