What is the solution for (dy}{dx}+\frac{3y)/x+2=3x,y(1)=1 ?

The solution for (dy}{dx}+\frac{3y)/x+2=3x,y(1)=1 is y=(3x^2)/5-x/2+9/(10x^3)

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(dy}{dx}+\frac{3y)/x+2=3x,y(1)=1

\frac{d y}{d x} + \frac{3 y}{x} + 2 = 3 x, y (1) = 1

y = \frac{3 x ^{2}}{5} - \frac{x}{2} + \frac{9}{10 x ^{3}}

Solution steps

\frac{d y}{d x} + \frac{3 y}{x} + 2 = 3 x

Solve linear ODE:

y = \frac{3 x ^{2}}{5} - \frac{x}{2} + \frac{9}{10 x ^{3}}

y = \frac{3 x ^{2}}{5} - \frac{x}{2} + \frac{9}{10 x ^{3}}

\frac{d}{d x} (3 x^{2} + 5 x - 2)

\int 2 tan^{5} (4 x) d x

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e - 4 x

\frac{2}{( 4 s ^{2} - 8 s )}

\frac{d}{d x} (sin (x) + arcsin (x))

What is the solution for (dy}{dx}+\frac{3y)/x+2=3x,y(1)=1 ?
The solution for (dy}{dx}+\frac{3y)/x+2=3x,y(1)=1 is y=(3x^2)/5-x/2+9/(10x^3)