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1-) Consider the following differential equation, y''(x)-e^(y'(x))^2+3y(x)=x. Which of following statements below is correct? a) Fourth order, linear. b) Fourth order, nonlinear. c) Third order, linear. d) Third order, nonlinear. e) Second order, nonlinear. 2-) What is the solution of following initial value problem? \frac{dy}{dx} = \frac{x^2}{y}, \quad y(0) = 1. a) y(x) = \sqrt{x^2+1} b) y(x) = \sqrt{x^2-1} c) y(x) = \sqrt{x^2+1} d) y(x) = \sqrt{x^2-1} e) y(x) = \sqrt{x^2+1}

          1-) Consider the following differential equation,
y''(x)-e^(y'(x))^2+3y(x)=x.
Which of following statements below is correct?
a) Fourth order, linear.
b) Fourth order, nonlinear.
c) Third order, linear.
d) Third order, nonlinear.
e) Second order, nonlinear.
2-) What is the solution of following initial value problem?
\frac{dy}{dx} = \frac{x^2}{y}, \quad y(0) = 1.
a) y(x) = \sqrt{x^2+1}
b) y(x) = \sqrt{x^2-1}
c) y(x) = \sqrt{x^2+1}
d) y(x) = \sqrt{x^2-1}
e) y(x) = \sqrt{x^2+1}

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1-) Consider the following differential equation,
y”(x)-e^(y'(x))^2+3y(x)=x.
Which of following statements below is correct?
a) Fourth order, linear.
b) Fourth order, nonlinear.
c) Third order, linear.
d) Third order, nonlinear.
e) Second order, nonlinear.
2-) What is the solution of following initial value problem?
(dy)/(dx) = (x^2)/(y), y(0) = 1.
a) y(x) = √(x^2+1)
b) y(x) = √(x^2-1)
c) y(x) = √(x^2+1)
d) y(x) = √(x^2-1)
e) y(x) = √(x^2+1)

Added by Rhonda C.

Calculus: Early Transcendentals

James Stewart 8th Edition

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06/15/2023

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This is a third order differential equation, and it is nonlinear because of the term (y''(x))^(2). Show more…

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1-) Consider the following differential equation, y'''(x)-e^(x)(y''(x))^(2)+3y(x)=x. Which of the following statements below is correct? a) Fourth order, linear. b) Fourth order, nonlinear. c) Third order, linear. d) Third order, nonlinear. e) Second order, nonlinear. 2-) What is the solution of the following initial value problem? (dy)/(dx)=(x^(2))/(y^(2)), y(0)=1 a) y(x)= oot(3)(x^(2)+1) b) y(x)= oot(3)(x^(2)-1) c) y(x)= oot(3)(x^(3)+1) d) y(x)= oot(3)(x^(3)-1) e) y(x)=sqrt(x^(3)+1) l- Consider the following differential equation yx-eyx+3(x=x Which of the following statements below is correct? a) Fourth order, linear b) Fourth order, nonlinear c) Third order linear d) Third order, nonlinear e) Second order, nonlinear 2-) What is the solution of the following initial value problem? y0=1. yx={x+1 byx=/x-1 cx=+1 y(x=/-1 eyx=+1

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