# The number of characteristic curves of the PDE [closed]

The number of characteristic curves of the PDE $(x^2+2y)u_{xx}+(y^3-y+x)u_{yy}+x^2(y-1)u_{xy}+3u_x+u=0$ passing through the point $x =1$, $y =1$ is
1. $0$
2. $1$
3. $2$
4. $3$

-

## closed as off-topic by This is much healthier., Norbert, amWhy, Thomas, studiosusJul 8 '14 at 14:37

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Norbert, amWhy, Thomas, studiosus
If this question can be reworded to fit the rules in the help center, please edit the question.

Given a second order linear PDE of the type you ask about, written in the form $$au_{xx}+2bu_{xy}+cu_{yy}+du_x+eu_y+fu=g,$$ the characteristics are the (real) solutions of the ODE $$\frac{dy}{dx}=\frac{1}{a}(-b\pm\sqrt{b^2-ac}).$$ By identifying the values of $a,b,c$ at $(x,y)=(1,1)$, can you see how many real solutions there are in your case?