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Exercise

$y''+16y=0$

Step-by-step Solution

Learn how to solve differential equations problems step by step online. Solve the differential equation y^''+16y=0. Obtain the characteristic equation. Find the solutions to the quadratic equation r^{2}+16=0. Of the complex solutions, take only the positive solution (the one where the coefficient of i is greater than 0). Express the complex root (4i) in the form r=a+bi where a and b are constants.
Solve the differential equation y^''+16y=0

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Final answer to the exercise

$y=C_0\cos\left(4x\right)+C_1\sin\left(4x\right)$

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equations
  • Homogeneous Differential Equation
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  • Product of Binomials with Common Term
  • FOIL Method
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Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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