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

The solution for (2x+3)(dy)/(dx)=y+(2x+3)^{1/2} is y= 1/2 ln(2x+3)(2x+3)^{1/2}+c_{1}(2x+3)^{1/2}

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(2x+3)(dy)/(dx)=y+(2x+3)^{1/2}

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

y = \frac{1}{2} ln (2 x + 3) (2 x + 3)^{\frac{1}{2}} + c_{1} (2 x + 3)^{\frac{1}{2}}

Solution steps

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

Solve linear ODE:

y = \frac{1}{2} ln (2 x + 3) (2 x + 3)^{\frac{1}{2}} + c_{1} (2 x + 3)^{\frac{1}{2}}

y = \frac{1}{2} ln (2 x + 3) (2 x + 3)^{\frac{1}{2}} + c_{1} (2 x + 3)^{\frac{1}{2}}

y = - \frac{4}{5 x ^{5}} + \frac{15}{4 x ^{4}}

f (x) = x^{2} + 21

\int \frac{1}{( x + 3 ) ^{2} ( x - 2 )} d x

\frac{d}{d x} (x^{2} 2^{x})

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

What is the solution for (2x+3)(dy)/(dx)=y+(2x+3)^{1/2} ?
The solution for (2x+3)(dy)/(dx)=y+(2x+3)^{1/2} is y= 1/2 ln(2x+3)(2x+3)^{1/2}+c_{1}(2x+3)^{1/2}