Question

NOU134362937: The order of differential equation
d^2y/dx^2+2 dy/dx d^3y/dx^3 + x=0 is __________
a. 1
b. 3
c. 4
d. 2

Answer 1

ANSWER on Question #77975 – Math – Differential Equations

QUESTION

The order of differential equation

$$\frac {d ^ {2} y}{d x ^ {2}} + 2 \cdot \frac {d y}{d x} \cdot \frac {d ^ {3} y}{d x ^ {3}} + x = 0 \text{ is }$$ $$(a) \ 1 \quad (b) \ 3 \quad (c) \ 4 \quad (d) \ 2$$

SOLUTION

By the definition, the order of a differential equation is the order of the highest order derivative present in the equation.

In our case,

$$\frac {d ^ {2} y}{d x ^ {2}} + 2 \cdot \frac {d y}{d x} \cdot \frac {d ^ {3} y}{d x ^ {3}} + x = 0 \text{ is third order since the highest derivative is } \frac {d ^ {3} y}{d x ^ {3}}.$$

Conclusion, the order of the differential equation

$$\frac {d ^ {2} y}{d x ^ {2}} + 2 \cdot \frac {d y}{d x} \cdot \frac {d ^ {3} y}{d x ^ {3}} + x = 0 \text{ is } (b) 3$$

ANSWER: (b) 3

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