I have the exercise below where $x(0)=5$:
$\frac{dx}{dt}=\frac{e^{3t}}{x}$
This obviously results in (Unless I am wrong!) to:
$\int xdx = \int e^{3t}dt$ $\frac{1}{2}x^2=\frac{1}{3}e^{3t}+C$ Multiply by $2$: $x^2=\frac{2}{3}e^{3t}+2C$ $x=\sqrt{\frac{2}{3}e^{3t}+2C}$
No using $x(0)=5$ to find actual value of the constant: $25=\frac{2}{3}+2C$ $25=\frac{2+6C}{3}$
I get $C=\frac{73}{6}$ so $2C$ will be $\frac{144}{6}$
So my final answer is: $x=\sqrt{\frac{2}{3}e^{3t}+\frac{146}{6}}$
The answer in the end of the book is given as:
$x=\frac{1}{3}\sqrt{219+6e^{3t}}$
I tried this exercise quite a few time but I can't get the real answer. Could someone please tell me what I am doing wrong here?