Question

The order of differential equation d2y/dx2+2dy/dxd3y/dx3+x=0 is __________

Answer 1

Answer on Question #69665 – Math – Differential Equations

Question

The order of differential equation $d2y/dx^2 + 2dy/dxd^3y/dx^3 + x = 0$ is

Solution

We have differential equation

$$\frac {d ^ {2} y}{d x ^ {2}} + 2 \frac {d y}{d x} \cdot \frac {d ^ {3} y}{d x ^ {3}} + x = 0.$$

It can be written as follows:

$$y ^ {\prime \prime} + 2 y ^ {\prime} y ^ {\prime \prime \prime} + x = 0.$$

The differential equation $y'' + 2y'y''' + x = 0$ is third order since the highest derivative is $y'''$ or the third derivative.

Answer: The order of differential equation $\frac{d^2y}{dx^2} + 2\frac{dy}{dx} \cdot \frac{d^3y}{dx^3} + x = 0$ is 3.

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