Exact Differential Equations Solve (2x + \sin y) dx +

gorovogpg 2021-12-30 Answered
Exact Differential Equations Solve (2x+siny)dx+(xcosy+4y3)dy=0
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Expert Answer

veiga34
Answered 2021-12-31 Author has 32 answers
(2x+siny)dx+(xlny+4y3)dy=0
M dx+N dy=0
My=Nx
My=y(2x+siny)=lny
Nx=x(xlny+4y3)=lny
My=Nx
Hence given DE is exact
(2x+siny)dx+4y3dy
2xdx+sinydx+4y3dy=c
α×x22+siny(x)+4×y44
x2+xsiny+y4=c
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Paul Mitchell
Answered 2022-01-01 Author has 40 answers
2xdx+(sinydx+xcosydy)+4y3dy=0
α(x2)+α(xsiny)+α(y4)=0
α(x2+xsiny+y4)=0
Integrating both side we get,
x2+xsiny+y4=c
Hence the required solution is
x2+xsiny+y4=c
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karton
Answered 2022-01-09 Author has 439 answers

2xdx+(sinydx+xcosydy)+4y3dy=0α(x2)+α(xsiny)+α(y4)=0α(x2+xsiny+y4)=0x2+xsiny+y4=cx2+xsiny+y4=c

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