## Related questions with answers

Question

Find the differential equation of the given family. Find the orthogonal trajectories of the family. Use a graphing utility to graph both families on the same set of coordinate axes.

$y = c _ { 1 } x$

Solution

VerifiedStep 1

1 of 4Let's first find the differential equation of the given family.

$y = c_1 x.$

Express the constant $c_1$ from the equation.

$c_1 = \dfrac{y}{x}.$

Put the constant into the derivative.

$\begin{align*} \dfrac{dy}{dx} &= c_1 \end{align*}$

$\color{#4257b2} \boxed{ \dfrac{dy}{dx} = \dfrac{y}{x} }$

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