# 2nd Year Engineering Maths ODE's (1 Viewer)

#### Thatstudentm9

##### Member
hey guys i need help with this question i would appreciate it highly if you can your full working out:

basically the question is saying to solve first order separable differential equation

i) lny^x*y'=3x^2*y

i understand you separate the variable i.e x on side y on the other being separable differential equation you integrate both sides and solve for y. I keep getting the wrong answer.

thanks

#### blyatman

##### Well-Known Member
Your equation isn't very clear. Is this the ODE you're trying to solve?
$\bg_white \ln(y^x)\frac{dy}{dx}=3x^2y$

#### Drongoski

##### Well-Known Member
If so:
$\bg_white xlny\frac{dy}{dx} = 3x^2y \\ \\ \therefore lny \frac{dy}{dx} = 3xy \\ \\\frac{lny}{y}dy = 3xdx \\ \\ \therefore \int \frac{lny}{y} dy = \int 3xdx \\ \\ \frac{1}{2} (lny)^2 = \frac{3x^2}{2} + \frac{C}{2}\\ \\ (lny)^2 = 3x^2 + C \\ \\ lny = \pm\sqrt{3x^2+C}\\ \\ \therefore y = e^{\pm \sqrt{3x^2 + C}}$

Don't know if correct

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wow, thnk