dyDo not solve the equation.= 2.x2 – y?4. Consider the differential equation:dydr.(a) Is the equation separable? If yes, write it in the form = f (x)g(y).(b) Is the equation linear? If yes, write it in the form + p(x)y = f(x).dydxdy(c) Is the equation exact? If yes, write it in the form M (x, y) + N(x, y)and show that it is exact.(d) Is the equation homogeneous? If yes, write it in the form 4 = F (4).dxdydx(e) Is the equation Bernoulli? If yes, write it in the form + p(x)y = f(x)y".

Answered: 4. Consider the differential equation:…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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dy
Do not solve the equation.
= 2.x2 – y?
4. Consider the differential equation:
dy
dr.
(a) Is the equation separable? If yes, write it in the form = f (x)g(y).
(b) Is the equation linear? If yes, write it in the form + p(x)y = f(x).
dy
dx
dy
(c) Is the equation exact? If yes, write it in the form M (x, y) + N(x, y)
and show that it is exact.
(d) Is the equation homogeneous? If yes, write it in the form 4 = F (4).
dx
dy
dx
(e) Is the equation Bernoulli? If yes, write it in the form + p(x)y = f(x)y".

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$\begin{array}{l} (4) \\ Consider the differential equation : \\ x y \frac{d y}{d x} = 2 x^{2} - y^{2} \\ To find : \\ (a) \\ Is the equation separable ? if Yes, write in the form \frac{d y}{d x} = f (x) g (y) . \\ (b) \\ Is the equation linear ? if Yes, write in the form \frac{d y}{d x} + p (x) y = f (x) . \\ (c) \\ Is the equation exact ? If Yes, write in the form of M (x, y) + N (x, y) \frac{d y}{d x} = 0 \\ and show that it is exact . \\ (d) \\ Is the equation homogeneous ? If Yes, write it in the form \frac{d y}{d x} = F (\frac{y}{x}) . \\ (e) \\ Is the equation Bernoulli ? If Yes, write it in the form \frac{d y}{d x} + p (x) y = f (x) y^{n} \end{array}$

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