Question

Determine the order, degree, linearity, unknown variable and independent  variable of the following differential equations

1. \(\frac{d y}{d x}=x y+3\)

2. \(\frac{d^{2} y}{d x^{2}}+7 \frac{d y}{d x}+y=9\)

3. \(\frac{d^{2} y}{d x^{2}}+7 \frac{d y}{d x}=\cos y \sin y\)

4. \(x^{3} \frac{d^{2} y}{d x}+x^{2} \frac{d y}{d x}+x^{2} y=\sin x\)

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Answer 1

Solutions ¥ is the order in equation. * While if all the We know that order of differential es is of highest derivative Degree is the power of highest derivative. * A Differential equation is linear dependent variable appear in linearly i.e. they are not involved with transcedental frs. and not multiplied together or squared. Dependent variables are dependent some variable known which are as independent vanables. ou * We know So, 0 dy xy+ 3 9 → degree=1, arder=1 non-linear dx / (1.ex.y) dependent variable y independent variable a dy dyz +7 +4292 order=2, degreeal, linear dependent variable=y Independent variable = x Z 3 dy dx² + 7 dy dx casysing order=2, degree = 1, Non-lineer (corysing) dependent variable ay Independent vanable 2x

2303 Sinse + x² dy are dy + xy dxa وزیر دار کر د T Order q degree = 1 Non-linear ( as sinx, & ex d²y Ex duom.) Independent variable an Dependent variable = Y у کار تیرا D Thank you!