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Chapter 8: Q 13-24MP (page 466)

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

x(yy" + y'2) = yy' Hint : Let u = yy'.

Short Answer

Expert verified

The solution of given differential equation is.

Step by step solution

01

Given information.

The differential equation is x(yy" + y'2) = yy' .

02

Differential equation.

When fand its derivatives are inserted into the equation, a solution is a function y=f(x) that solves the differential equation. The highest order of any derivative of the unknown function appearing in the equation is the order of a differential equation.

A differential equation of the form has general solution

03

Find the solution of the given differential equation.

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Most popular questions from this chapter

a) Show that∇⋅(er/r2)=0forr>0.

(b) Show that∇(1/r)=-er/r2.

Using Problems 29 and 31b show that equation (6.24) is correct.

Find the transform of

f(t)={sin(x-vt),t>x/v0,t<x/v

Where xand vare constants.

Find the shape of a mirror which has the property that rays from a point 0 on the axis are reflected into a parallel beam. Hint: Take the point 0 at the origin. Show from the figure that tanθ=2yx. Use the formula for tanθ2to express this in terms of tanθ=dydxand solve the resulting differential equation. (Hint: See Problem 16.)

Find the orthogonal trajectories of each of the following families of curves. In each case, sketch or computer plot several of the given curves and several of their orthogonal trajectories. Be careful to eliminate the constant from y'for the original curves; this constant takes different values for different curves of the original family, and you want an expression for y'which is valid for all curves of the family crossed by the orthogonal trajectory you are trying to find. See equations 2.10to 2.12.

(y-1)2=x2+k
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