Proving the general solution of a differential equation

**Punch** · December 18th 2011, 11:49 PM

Prove that the general solution to the differential equation, $\frac{dy}{dx}=\frac{k}{xhy}$ is $y^2=lnCx^n$ where $k, h, C and n$ are constants.

$\frac{dy}{dx}=\frac{k}{xhy}$

$\int{y}dy=\int\frac{A}{x}dx$ where $A=\frac{k}{h}$

$\frac{1}{2}y^2=Alnx+C$

how can I twit the equation further?

**FernandoRevilla** · December 19th 2011, 12:07 AM

Originally Posted by Punch

$\frac{1}{2}y^2=Alnx+C$ how can I twit the equation further?

$y^2=2A\ln x+2C=\ln x^{2A}+\ln K=\ln (Kx^{2A})=\ln (Kx^n)$

**Punch** · December 19th 2011, 12:09 AM

Originally Posted by FernandoRevilla

Express the equation in the form $hy\;dy-\frac{kdx}{x}=0$ (separated variables) .

Alright, then i get $h\frac{y^2}{2}=klnx + C$ which I still dont see how I can further transform this

**Punch** · December 19th 2011, 12:10 AM

Originally Posted by FernandoRevilla

$y^2=2A\ln x+2C=\ln x^{2A}+\ln K=\ln (Kx^{2A})=\ln (Kx^n)$

Oh! I see, so I just have to insert a lnC' to replace C and that does the trick!

Thread: Proving the general solution of a differential equation

LinkBack

Thread Tools

Display

Proving the general solution of a differential equation

Re: Proving the general solution of a differential equation

Re: Proving the general solution of a differential equation

Re: Proving the general solution of a differential equation

Similar Math Help Forum Discussions

General solution of a differential equation

general solution of a differential equation

General solution to differential equation

General Solution to Differential Equation

General Solution of Differential Equation

Search Tags