Solving \frac{dy}{d \theta}+y \cos \theta=\frac 12 \sin 2 \theta with

Ethen Wong

Ethen Wong

Answered question

2022-01-26

Solving dydθ+ycosθ=12sin2θ with y(π2)=4

Answer & Explanation

Damian Roberts

Damian Roberts

Beginner2022-01-27Added 14 answers

y+ycos(θ)=12sin(2θ)
Multiply by integrating factor*** μ(θ)=esin(θ)
yesin(θ)+yesin(θ)cos(θ)=12esin(θ)sin(2θ)
(yesin(θ))=esin(θ)sin(θ)cos(θ)
Integrate
yesin(θ)=esin(θ)sin(θ)cos(θ)dθ
Substitute u=sin(θ)
yesin(θ)=euudu
yesin(θ)=eeu+K
y=sin(θ)1+Kesin(θ)
Apply the initial condition
*** there is a formula for the integrating factor for an equation y+p(x)y=q(x) the integrating factor is μ=ep(x)dx

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