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Объяснение:

1.

y'=2xcos²y

[tex]\frac{dy}{dx} =2xcos^2(y)\\dy=2xcosx^{2} (y)dx\\\frac{dy}{cosx^{2} (y)} =2xdx\\\\[/tex]

∫ [tex]\frac{1}{cos^2(y)}dy[/tex]=∫ [tex]2xdx[/tex]

[tex]\frac{sin(y)}{cos(y)} = x^{2} +C[/tex]

⇒sin(y)-x²cos(y)= C cos (y), y=[tex]\frac{\pi }{2}[/tex]

2.

y'=[tex]e^{2x}[/tex]+4x

[tex]\frac{dx}{dy} =[/tex][tex]e^{2x}[/tex]+4x

dy=([tex]e^{2x}[/tex]+4x)dx

∫1dy=∫[tex]e^{2x}[/tex]+4xdx

y=[tex]\frac{e^{2x} }{2} +2x^{2} +C[/tex], C= const