What is the solution for y^'=((e^{(x/3)}+y))/2 ?

The solution for y^'=((e^{(x/3)}+y))/2 is y=-3e^{x/3}+c_{1}e^{x/2}

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y^'=((e^{(x/3)}+y))/2

y^{^{'}} = \frac{( e ^{(\frac{x}{3})} + y )}{2}

y = - 3 e^{\frac{x}{3}} + c_{1} e^{\frac{x}{2}}

Solution steps

y^{'} (x) = \frac{( e ^{(\frac{x}{3})} + y )}{2}

Solve linear ODE:

y = - 3 e^{\frac{x}{3}} + c_{1} e^{\frac{x}{2}}

y = - 3 e^{\frac{x}{3}} + c_{1} e^{\frac{x}{2}}

What is the solution for y^'=((e^{(x/3)}+y))/2 ?
The solution for y^'=((e^{(x/3)}+y))/2 is y=-3e^{x/3}+c_{1}e^{x/2}