What is the solution for (dy)/(dx)=x+6y,y(0)=7 ?

The solution for (dy)/(dx)=x+6y,y(0)=7 is y=-(6x+1)/(36)+253/36 e^{6x}

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(dy)/(dx)=x+6y,y(0)=7

\frac{d y}{d x} = x + 6 y, y (0) = 7

y = - \frac{6 x + 1}{36} + \frac{253}{36} e^{6 x}

Solution steps

\frac{d y}{d x} = x + 6 y

Solve linear ODE:

y = - \frac{6 x + 1}{36} + \frac{253}{36} e^{6 x}

y = - \frac{6 x + 1}{36} + \frac{253}{36} e^{6 x}

5 x y \frac{d y}{d x} = 2

\int \frac{1}{( x + 4 ) ^{5}} d x

\int x x + 7 d x

x \to - 2 + lim (x)

\frac{d}{d x} (\frac{sin ( 2 x + 1 )}{2 x + 1})

What is the solution for (dy)/(dx)=x+6y,y(0)=7 ?
The solution for (dy)/(dx)=x+6y,y(0)=7 is y=-(6x+1)/(36)+253/36 e^{6x}