What is the solution for (dy)/(dx)=x+2y,y(0)=6 ?

The solution for (dy)/(dx)=x+2y,y(0)=6 is y=-(2x+1)/4+25/4 e^{2x}

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(dy)/(dx)=x+2y,y(0)=6

\frac{d y}{d x} = x + 2 y, y (0) = 6

y = - \frac{2 x + 1}{4} + \frac{25}{4} e^{2 x}

Solution steps

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

Solve linear ODE:

y = - \frac{2 x + 1}{4} + \frac{25}{4} e^{2 x}

y = - \frac{2 x + 1}{4} + \frac{25}{4} e^{2 x}

x \to 0 lim (\frac{π x ^{2} + 2}{x})

\frac{\partial}{\partial x} (ln ∣ x ∣)

x \to 0 lim (3 x ln (x))

x \to 3 lim (8 x^{2} + 9)

What is the solution for (dy)/(dx)=x+2y,y(0)=6 ?
The solution for (dy)/(dx)=x+2y,y(0)=6 is y=-(2x+1)/4+25/4 e^{2x}