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Chapter 1: Q1RP (page 1)

In problems 1-6, identify the independent variable, dependent variable, and determine whether the equation is linear or nonlinear.

5dxdt+5x2+3=0

Short Answer

Expert verified

⦁ The Independent variable is t.

⦁ The dependent variable is x.

⦁ The equation is Non-linear.

Step by step solution

01

Identifying the dependent and independent variables

Clearly, the independent variable is t while the dependent variable is x.

02

Determining whether the equation is linear or nonlinear

The equation is a quadratic equation has power of x2.

So, the equation is Non-linear.

Hence, the Independent variable is t. The dependent variable is x. And the equation is Non-linear.

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Most popular questions from this chapter

In Problems 9–20, determine whether the equation is exact.

If it is, then solve it.

et(y - t)dt +(1 +et)dy = 0

Show that ϕ(x)=Ce3x+1is a solution tolocalid="1663944867164" dydx-3y=-3for any choice of the constant C. Thus,Ce3x+1 is a one-parameter family of solutions to the differential equation. Graph several of the solution curves using the same coordinate axes.

In problems 1-6, identify the independent variable, dependent variable, and determine whether the equation is linear or nonlinear.

6-t3(d2vdt2)+3v-lnt=dvdt

Verify that ϕ(x)=2(1-cex),where c is an arbitrary constant, it is a one-parameter family of solutions to dydx=y(y-2)2. Graph the solution curves corresponding to c=0,±1,±2 using the same coordinate axes.

In Problem 19, solve the given initial value problem

y'''−y''−4y'+4y=0y(0)=−4y'(0)=−1y''(0)=−19
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