What is the solution for (3x+2)f^'(x)=6f(x) ?

The solution for (3x+2)f^'(x)=6f(x) is f(x)=9e^{c_{1}}x^2+12e^{c_{1}}x+4e^{c_{1}}

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(3x+2)f^'(x)=6f(x)

(3 x + 2) f^{^{'}} (x) = 6 f (x)

f (x) = 9 e^{c_{1}} x^{2} + 12 e^{c_{1}} x + 4 e^{c_{1}}

Solution steps

(3 x + 2) f^{'} (x) = 6 f (x)

Solve separable ODE:

f (x) = 9 e^{c_{1}} x^{2} + 12 e^{c_{1}} x + 4 e^{c_{1}}

f (x) = 9 e^{c_{1}} x^{2} + 12 e^{c_{1}} x + 4 e^{c_{1}}

\frac{d y}{d t} = 0.1 y, y (0) = 350

5 x - 8 y (x^{2} - 1) y^{^{'}} = 0

y^{^{'}} - \frac{2}{x} y = - \frac{2}{x}

\frac{d y}{d x} = e^{3 y + 6 x}

\frac{d x}{d t} = \frac{5}{x}, x (0) = 2

What is the solution for (3x+2)f^'(x)=6f(x) ?
The solution for (3x+2)f^'(x)=6f(x) is f(x)=9e^{c_{1}}x^2+12e^{c_{1}}x+4e^{c_{1}}