PDE Part - 2 CSIR NET July 2026 Memory-based Question

[00:00:00]Hello students, welcome to the part 11 of the memory based question. Today I will explain you the partial differential equations related to the CSR net July 2026. Myself Dr. Harishkar you can follow and subscribe my YouTube channel. The question that I had received from the student is the if the partic if the particular integral of the differential equation is x power a y power b log y power c then the value of the a b and c is equal to very simple question you can see I can write the given differential equation in the form of zprime minus 3 / y z prime which is equal to x x y^ 2 clearly say it look like say linear partial differential equation or you can because it's only the differential equation y so you can consider as a linear ordinary differential equation I can simply consider z ddash to be the t equation it's a t prime minus fine t = x y² fine now I can find the integrating factor it is e power p dx - 3 / y into dy that will be 1 / yq. So therefore your solution will be t into integrating factor which is equal to integration of the right hand side into integrating factor with respect to y. So you have to integrate with respect to y. x is outside 1 / y is my ln of y.

[00:01:45]I can multiply by Y cube. It's into Y.

[00:01:48]Now what is the value of the T? T is my Z prime. Z prime is with respect to Y.

[00:01:53]So how you can find the value of the Z?

[00:01:55]I can take an X is outside. It's a y into ln of the y will be x into I can integrate by part first function ln of y into y4 / 4 minus derivative of the ln y into integration z 4 / 4 it's a cube cube integration it's a 4 / 16 - y4 divided by 16. If you open that, it's a 1 / 4 x ln of y into y power 4 minus x y4 / 16 because this is one of the particular solution. Now you can compare what is the a is a coefficient power of the x 1 b power of the y 4 c power of the log of y. Y is my one. So c is my one. So what is the answer of the A, B and C? Six is the right answer of the problem.

[00:03:03]Students questions let me know in the comment box. So if you have more questions on the PD or the ordinary differentials, send me in the comment box. I will upload the solution for you again. Till then you can subscribe my YouTube channels, share my this video with your friends and like and comments on the video as well. Best of luck students.