Exercise · ZW-DIFFERENTIAL-EQUATION-003 · ★☆☆ Basic
Differentiating \(y=Ce^{3x}\) and eliminating the constant \(C\) gives the equation:
Choose one option.
Show answer
- C. \(y'=3y\)
Explanation
Since \(y'=3Ce^{3x}=3y\), the constant disappears. \(y'=Cy\) still contains \(C\).
Review the concept: Differential equation
A differential equation is an equation \(F=0\) whose unknown is a function \(y\) and which relates it to one or more of its derivatives.
\[F\left(x,\,y,\,y',\,\dots,\,y^{(n)}\right)=0\]
More practice problems: differential equation
- ZW-DIFFERENTIAL-EQUATION-001 Which of the following is a differential equation?
- ZW-DIFFERENTIAL-EQUATION-002 In (dy)/(dt)=-0.5 y, which is the independent variable?
- ZW-DIFFERENTIAL-EQUATION-004 Which of the following is NOT a differential equation?
- ZW-DIFFERENTIAL-EQUATION-005 Differentiating y=x^2+C and eliminating C gives:
- ZW-DIFFERENTIAL-EQUATION-006 Which of the following differential equations involves partial derivatives?
- ZW-DIFFERENTIAL-EQUATION-007 Which function satisfies the equation y''+y=0?
- ZW-DIFFERENTIAL-EQUATION-008 If the rate of change of a population P with respect to time is proportional to P, the model is:
- ZW-DIFFERENTIAL-EQUATION-009 Solving y'=2y means finding:
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