What is the solution for x(dy)/(dx)+(3x+1)y=e^{(-3x)},y(1)=e^7 ?

The solution for x(dy)/(dx)+(3x+1)y=e^{(-3x)},y(1)=e^7 is y= 1/(e^{3x)}+(e^{10}-1)/(e^{3x)x}

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x(dy)/(dx)+(3x+1)y=e^{(-3x)},y(1)=e^7

x \frac{d y}{d x} + (3 x + 1) y = e^{(- 3 x)}, y (1) = e^{7}

y = \frac{1}{e ^{3 x}} + \frac{e ^{10} - 1}{e ^{3 x} x}

Solution steps

x \frac{d y}{d x} + (3 x + 1) y = e^{(- 3 x)}

Solve linear ODE:

y = \frac{1}{e ^{3 x}} + \frac{e ^{10} - 1}{e ^{3 x} x}

y = \frac{1}{e ^{3 x}} + \frac{e ^{10} - 1}{e ^{3 x} x}

What is the solution for x(dy)/(dx)+(3x+1)y=e^{(-3x)},y(1)=e^7 ?
The solution for x(dy)/(dx)+(3x+1)y=e^{(-3x)},y(1)=e^7 is y= 1/(e^{3x)}+(e^{10}-1)/(e^{3x)x}