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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

By using Laplace transforms, solve the following differential equations subject to the given initial conditions.

y¨+4y˙+5y=2e-2tcost,y0=0,y˙0=3

The speed of a particle on the x axis, x≥0, is always numerically equal to the square root of its displacement x. If x=0when t=0, find x as a function of t. Show that the given conditions are satisfied if the particle remains at the origin for any arbitrary length of time t0and then moves away; find x for t>t0for this case.

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 (2.10)to (2.12)

x2+y2=cost.

By using Laplace transforms, solve the following differential equations subject to the given initial conditions.

y"-4y'+4y=4, ∑0=0,ψ0=-2

Obtain L(te-atcosbt)
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