Solve differential equation(cos^2y)/(4x+2)dy= ((cosy+siny)^2)/(sqrt(x^2+x+3))dx

Chaya Galloway 2021-03-07 Answered

Solve differential equation cos2y4x+2dy=(cosy+siny)2x2+x+3dx

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Expert Answer

mhalmantus
Answered 2021-03-08 Author has 106 answers

cos2y4x+2dy=cos2y+sin2y+2sinycosyx2+x+3dx
cos2y4x+2dy=1+sin2yx2+x+3dx
cos2y1+sin2ydy=4x+2x2+x+3dx
Integrating on both sides
cos2y1+sin2ydy=4x+2x2+x+3dx
4x+2x2+x+3dx
Let x2+x+3=u2
2x+1dx=2udu
4x+2dx=4udu
4x+2x2+x+3dx=4u duudu
=4du=4u+c
=4x2+x+3+c
cos2y1+sin2yy
Let t=1+sin2y
Differentiating
dt=2cos2y
cos2y1+sin2ydy=12dtt
=121tdt =12lnt+K
12ln(1+sin2y)+k
cos2y1+sin2ydy=4x+2x2+x+3dx
4x2+x+3=12ln(1+sin2y)+c

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Jeffrey Jordon
Answered 2021-12-25 Author has 2581 answers

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