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Differential Equations · Question 19 of 67

Question 19

EasyOriginal question

Which is the particular solution of dydx=2x\frac{dy}{dx} = 2x with y=3y = 3 when x=0x = 0?

Options for question 19

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. The general solution is y=x2+Cy = x^2 + C.

  2. y(0)=3y(0) = 3 gives C=3C = 3, so the particular solution is y=x2+3y = x^2 + 3.

Worth noting

y=x2+Cy = x^2 + C is the general solution; the condition is what picks one curve from it.

Concept
A particular solution from a condition
Typical time
60 s
Your time
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The rule this testsGeneral and particular solutions
Practise this chapter →

Ten questions from Differential Equations, at your own pace.

Practise this chapter →

Ten questions from Differential Equations, at your own pace.