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Lesson: Solving Initial Value Problems of Differential Equations

In this lesson, we will learn how to solve initial value problems of differential equations.

Worksheet • 22 Questions

Q1:

Find the solution for the following differential equation for 𝑦 ( 0 ) = 1 6 :

  • A 𝑦 = 5 + 1 1 𝑒 4 π‘₯
  • B 𝑦 = 5 + 1 1 𝑒 π‘₯
  • C 𝑦 = 5 + 1 1 𝑒 π‘₯ 4
  • D 𝑦 = 5 + 1 1 𝑒 βˆ’ 4 π‘₯

Q2:

The gradient of the tangent to a curve is ο„ž βˆ’ 𝑦 + 3 4 π‘₯ βˆ’ 4 . Find the equation of the curve given that the curve passes through the point ( 5 , 3 ) .

  • A βˆ’ 2 √ βˆ’ 𝑦 + 3 = 1 2 √ 4 π‘₯ βˆ’ 4 βˆ’ 2
  • B 2 √ βˆ’ 𝑦 + 3 = 2 √ 4 π‘₯ βˆ’ 4 βˆ’ 2
  • C βˆ’ √ βˆ’ 𝑦 + 3 = 1 4 √ 4 π‘₯ βˆ’ 4 βˆ’ 2
  • D βˆ’ 2 √ βˆ’ 𝑦 + 3 = 8 √ 4 π‘₯ βˆ’ 4 βˆ’ 2

Q3:

Find a particular solution for the following differential equation for which 𝑦 ( 0 ) = 1 2 :

  • A 𝑦 = 4 π‘₯ + 3 π‘₯ + 1 2 2
  • B 𝑦 = 8 π‘₯ + 3 π‘₯ + 1 2 2
  • C 𝑦 = 8 π‘₯ + 3 π‘₯ 2
  • D 𝑦 = 4 π‘₯ + 3 π‘₯ 2
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