Solve differential equation dy/dx-12x^3y=x^3

Ernstfalld 2021-02-13 Answered
Solve differential equation dy/dx12x3y=x3
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Expert Answer

Benedict
Answered 2021-02-14 Author has 108 answers

dy/dx=x3+12x3y
dy/dx=x3(1+12y)
dy/((1+12y))=x3dx
Taking Integration on both sides, we get
dy/(1+12y)=x3dx
Using u− substitution rule
Let u=1+12y
du=12dy
dy=1/12du
Substituting the values above
dy/(1+12y)=x3dx
1/12(du)/u=x4/4+C
Integrating
1/12u=x4/4+C
1/12ln(1+12y)=x4/4+C
Isolating y
ln(1+12y)=3x4+12C
ln(1+12y)=3x4+C1
1+12y=e3x4+C1
y=(e3x4+C11)/12
y=(e3x4+C1)/121/12

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