Match each differential equation with its family of solutions.(a) x dydx = y (i) y = x2

Chapter 8, Problem 1

(choose chapter or problem)

Match each differential equation with its family of solutions.

(a) $x\ \frac{dy}{dx}\ =\ y$ _______ (i) $y=x^2\ +\ C$

(b) $y^{\prime\prime}\ =\ 4y$_______ (ii) $y=C_1\sin\ 2x\ +\ C_2\ \cos\ 2x$

(d) $\frac{d^2y}{dx^2}\ =\ -4y$ ______ (iv) $y\ =\ Cx$

Equation Transcription:

$x\frac{dy}{dx}\ \ =\ \ y$

$y\ \ =\ \ {x}^{2}\ \ +\ \ C$

$y''\ \ =\ \ 4y$

$y\ =\ {C}_{1}\ \ sin\ \ 2x\ \ +\ \ {C}_{2}\ \ cos\ \ 2x$

$\frac{dy}{dx}\ \ =\ \ 2x$

$y\ \ =\ \ {C}_{1}{e}^{2x}\ \ +\ \ {C}_{2}{e}^{-2x}$

$\frac{{d}^{2}y}{d{x}^{2}}\ \ =\ \ -4y$

$y\ =\ Cx$

Text Transcription:

x frac{dy}{dx} = y

y = x^2 + C

y’’ = 4y

y = C_1 sin 2x + C_2 cos 2x

frac{dy}{dx} = 2x

y = C_1e^2x + C_2e^-2x

frac{d^2y}{dx^2} = -4y

y = Cx

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