Lição de casa da aula: Equações Diferenciais Lineares de Primeira Ordem Mathematics

Nesta atividade, nós vamos praticar a resolver equações diferenciais lineares de primeira ordem.

Q1:

Resolva a equaΓ§Γ£o diferencial dd𝑦π‘₯+𝑦=π‘₯.

  • A𝑦=π‘₯βˆ’1+𝑒CοŠ±ο—
  • B𝑦=π‘₯βˆ’1+𝑒C
  • C𝑦=π‘₯𝑒2+π‘’οŠ¨οŠ±ο—οŠ±ο—C
  • D𝑦=π‘₯𝑒2+π‘’οŠ¨ο—οŠ±ο—C
  • E𝑦=π‘₯+1+𝑒CοŠ±ο—

Q2:

Resolva a equaΓ§Γ£o diferencial π‘₯𝑦π‘₯+𝑦=π‘₯π‘₯ddln, onde π‘₯>0, sujeita Γ  condiΓ§Γ£o 𝑦(1)=0.

  • A𝑦=π‘₯2π‘₯βˆ’π‘₯4+12π‘₯ln
  • B𝑦=π‘₯π‘₯βˆ’π‘₯4+14π‘₯ln
  • C𝑦=π‘₯4π‘₯βˆ’π‘₯4+14π‘₯ln
  • D𝑦=π‘₯2π‘₯+π‘₯4+14π‘₯ln
  • E𝑦=π‘₯2π‘₯βˆ’π‘₯4+14π‘₯ln

Q3:

Resolva a equaΓ§Γ£o diferencial π‘₯𝑦π‘₯+π‘₯𝑦=1dd, para π‘₯>0, sujeita Γ  condiΓ§Γ£o 𝑦(1)=2.

  • A𝑦=π‘₯+2π‘₯ln
  • B𝑦=π‘₯βˆ’2+2π‘₯lnln
  • C𝑦=π‘₯+22π‘₯ln
  • D𝑦=π‘₯π‘₯ln
  • E𝑦=βˆ’1π‘₯+3

Q4:

Resolva a equaΓ§Γ£o diferencial π‘₯𝑦π‘₯=𝑦+π‘₯π‘₯ddsen sujeita Γ  condiΓ§Γ£o 𝑦(πœ‹)=0.

  • A𝑦=π‘₯π‘₯+π‘₯cos
  • B𝑦=π‘₯π‘₯βˆ’π‘₯cos
  • C𝑦=βˆ’π‘₯π‘₯+π‘₯cos
  • D𝑦=π‘₯π‘₯cos
  • E𝑦=βˆ’π‘₯π‘₯βˆ’π‘₯cos

Q5:

Resolva a equaΓ§Γ£o diferencial 𝑑𝑒𝑑=𝑑+3𝑒dd sujeita Γ  condiΓ§Γ£o 𝑒(2)=4.

  • A𝑒=π‘‘οŠ¨
  • B𝑒=βˆ’π‘‘+π‘‘οŠ©
  • C𝑒=𝑑5+1285π‘‘οŠ¨οŠ©
  • D𝑒=βˆ’π‘‘+π‘‘οŠ¨οŠ©
  • E𝑒=βˆ’π‘‘βˆ’π‘‘οŠ¨οŠ©

Q6:

Resolva a equaΓ§Γ£o diferencial 𝑑𝑦𝑑+3𝑑𝑦=√1+π‘‘οŠ¨οŠ¨dd, onde 𝑑>0.

  • A𝑦=13ο€Ή1+𝑑𝑑+π‘‘οŠ¨οŠ±οŠ©οŠ±οŠ©οŽ’οŽ‘C
  • B𝑦=13(1+𝑑)𝑑+π‘‘οŽ’οŽ‘οŠ±οŠ©οŠ±οŠ©C
  • C𝑦=13(1+𝑑)𝑑+π‘‘οŽ’οŽ‘οŠ±οŠ©οŠ±οŠ©C
  • D𝑦=13ο€Ή1+𝑑𝑑+π‘‘οŠ¨οŠ±οŠ©οŠ±οŠ©οŽ οŽ‘C
  • E𝑦=ο€Ή1+𝑑𝑑+π‘‘οŠ¨οŠ±οŠ©οŠ±οŠ©οŽ’οŽ‘C

Q7:

Resolva a equaΓ§Γ£o diferencial π‘₯𝑦π‘₯+𝑦=√π‘₯dd.

  • A𝑦=√π‘₯2+π‘₯C
  • B𝑦=25√π‘₯+π‘₯C
  • C𝑦=2√π‘₯3+π‘₯C
  • D𝑦=25√π‘₯+π‘₯C
  • E𝑦=2√π‘₯3+C

Q8:

Resolva a equaΓ§Γ£o diferencial 2π‘₯𝑦π‘₯+𝑦=2√π‘₯dd.

  • A𝑦=√π‘₯+√π‘₯C
  • B𝑦=√π‘₯+√π‘₯C
  • C𝑦=π‘₯+√π‘₯C
  • D𝑦=1+√π‘₯C
  • E𝑦=π‘₯+π‘₯C

Q9:

Resolva a equaΓ§Γ£o diferencial ο€Ήπ‘₯+1𝑦π‘₯+3π‘₯(π‘¦βˆ’1)=0dd sujeita Γ  condiΓ§Γ£o 𝑦(0)=2.

  • A𝑦=1+1(π‘₯+1)
  • B𝑦=1βˆ’1(π‘₯+1)
  • C𝑦=1+1(π‘₯+1)
  • D𝑦=1βˆ’5√5(π‘₯+1)
  • E𝑦=3+1(π‘₯+1)

Q10:

A equaΓ§Γ£o diferencial ddcosπ‘Ÿπ‘‘+π‘‘π‘Ÿ=π‘’οŠ±ο Γ© linear?

  • Asim
  • BnΓ£o

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