Find the complete integral of the partial differential equation and deduce the solution which passes through the curve

Asked Jan 08 '22 at 06:49

Active Jan 08 '22 at 06:49

Viewed 361 times

Find the complete integral of the partial differential equation $(p^2 + q^2)x = pz$ and deduce the solution which passes through the curve $x = 0, z^2 = 4y$.

I am able to find the complete solution which is : $z^2=a^2x^2+(ay+b)^2$ where $a$ and $b$ are some arbitrary constant. But I am not able to find the particular solution. Finding particular solution will require eliminating $a$ and $b$ but I am still getting one of the constant in my solution.

asked Jan 08 '22 at 06:49

user13556745

$(4y)^2=0^2a^2+(ay+b)^2$ what are $a$ and $b$ ? – JJacquelin Jan 08 '22 at 07:22
$a$ and $b$ are constants we get when we solve the partial diff eqn using Charpit's Method – user13556745 Jan 08 '22 at 08:47
Then what is your problem ? – JJacquelin Jan 08 '22 at 09:16
The solution containing $a$ and $b$ is general solution. I need the particular solution which passes through the given curve. Particular solutions shouldn't have arbitrary constants. I am not able to eliminate these $a$ and $b$. Pls read the ques again. – user13556745 Jan 08 '22 at 12:07
No, you don't have to eliminate $a$ and $b$. You have to find the numerical values of $a$ and $b$ and to put these values into the general solution. To find the values of $a$ and $b$, please read again my first comment. – JJacquelin Jan 08 '22 at 17:45
Does this answer your question? Singular solution of partial differential equation – Gonçalo Mar 19 '24 at 20:13

Find the complete integral of the partial differential equation and deduce the solution which passes through the curve

0 Answers0