What is the solution for y^'=xsin(x)+xcos(x) ?

The solution for y^'=xsin(x)+xcos(x) is y=-xcos(x)+sin(x)+xsin(x)+cos(x)+c_{1}

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y^'=xsin(x)+xcos(x)

y^{^{'}} = x sin (x) + x cos (x)

y = - x cos (x) + sin (x) + x sin (x) + cos (x) + c_{1}

Solution steps

y^{'} (x) = x sin (x) + x cos (x)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int x sin (x) + x cos (x) d x

\int x sin (x) + x cos (x) d x = - x cos (x) + sin (x) + x sin (x) + cos (x) + c_{1}

y = - x cos (x) + sin (x) + x sin (x) + cos (x) + c_{1}

What is the solution for y^'=xsin(x)+xcos(x) ?
The solution for y^'=xsin(x)+xcos(x) is y=-xcos(x)+sin(x)+xsin(x)+cos(x)+c_{1}