What is the solution for (dy)/(dx)=(4+3x)^4 ?

The solution for (dy)/(dx)=(4+3x)^4 is y= 1/15 (4+3x)^5+c_{1}

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(dy)/(dx)=(4+3x)^4

\frac{d y}{d x} = (4 + 3 x)^{4}

y = \frac{1}{15} (4 + 3 x)^{5} + c_{1}

Solution steps

\frac{d y}{d x} = (4 + 3 x)^{4}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (4 + 3 x)^{4}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int (4 + 3 x)^{4} d x

\int (4 + 3 x)^{4} d x = \frac{1}{15} (4 + 3 x)^{5} + c_{1}

y = \frac{1}{15} (4 + 3 x)^{5} + c_{1}

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x^{2} y^{^{''}} + 2 x y^{^{'}} - 6 y = 0

x \to - 2 - lim (\frac{1}{( x + 2 ) ^{5}})

\frac{d}{d x} (3 x^{6} e^{x})

x + 4 y = 25, x + 7 = y^{2}

What is the solution for (dy)/(dx)=(4+3x)^4 ?
The solution for (dy)/(dx)=(4+3x)^4 is y= 1/15 (4+3x)^5+c_{1}