Find the general solution of the differential equation. Use C for the constant of integration.
dy/dx= 4x + 3/x

Question

Find the general solution of the differential equation. Use C for the constant of integration.
dy/dx= 4x + 3/x

unklerhaukus · Answer

$$\frac{\mathrm dy}{\mathrm dx}=4x+3/x$$
separate the variables
$$\mathrm dy=(4x+3/x)\,\mathrm dx$$
now integrate both sides
$$\int\mathrm dy=\int(4x+3/x)\,\mathrm dx$$

anonymous · Answer

I had 2x^2+ 3ln(x) +C and idk why its wrong

unklerhaukus · Answer

that's right

$$y(x) = 2x^2+3\ln x+C$$

anonymous · Answer

but my homework says its wrong ;/ does the lnx have to be in absolute value

unklerhaukus · Answer

oh yeah, 
we can't take the log of a negative number, 
so the argument of the log should be an absolute value

$$y(x) = 2x^2+3\ln|x|+C$$

anonymous · Answer

okay hang on let me see if it takes that!

anonymous · Answer

can you help me with this one? 
 Find the general solution of the differential equation. Use C for the constant of integration.
dr/dp = 10sin(p)

anonymous · Answer

the previous one was right by the way! thanks :)

unklerhaukus · Answer

Oh good.

This one is the same idea, separate the variables, and integrate

anonymous · Answer

so it'd be 10xcos(p)+C..?

unklerhaukus · Answer

careful with your sign,

unklerhaukus · Answer

$$\int\sin=-\cos$$

unklerhaukus · Answer

@anarvizo