Which of the following differential equations is a linear equation of order \(3:\)
\[\begin{align}
&(a) \frac{d^3y}{dx^3}+\frac{d^2y}{dx^2}\frac{dy}{dx}+y=5x\\
&(b) \frac{d^3y}{dx^3}+\frac{d^2y}{dx^2}+y^2=x^2+3x\\
&(c) x\frac{d^3y}{dx^3}+\frac{d^2y}{dx^2}=e^x\\
&(d) \frac{d^2y}{dx^2}+\frac{dy}{dx}=\log{x}?
\end{align}\]

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If \(a\) and \(b\) are the order and the degree, respectively, of the differential equation
\[\left(\frac{d^{4}y}{dx^{4}}\right)^{8}-\left(\frac{dy}{dx}\right)^{25}+15=0,\]
what is the value of \(b-a?\)

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Which of the following differential equations has degree \(1 ?\)
\[\begin{align}
&\text{(a) } x^3\frac{d^2y}{dx^2}+(x+x^2)\left(\frac{dy}{dx}\right)^2+e^xy^3=2\sin x \\
&\text{(b) } y=2\frac{dy}{dx}+5\sqrt{1-\left(\frac{dy}{dx}\right)^2} \\
&\text{(c) } \sqrt{\frac{dy}{dx}+y}=x+4
\end{align}\]

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