Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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. $3$

how can i solve this problem.please help anybody

share|improve this question
add comment

1 Answer

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?

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.