Word Count : 222

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यह एक आंशिक अवकल समीकरण (PDE) है: \[ x^2 \frac{\partial^2 z}{\partial x^2} - y^2 \frac{\partial^2 z}{\partial y^2} + x \frac{\partial z}{\partial x} - y \frac{\partial z}{\partial y} = \ln x \] इस समीकरण को हल करने के लिए हम विभिन्न तरीकों का इस्तेमाल कर सकते हैं, जैसे कि गुणात्मक समाधान (method of characteristics), परिवर्तनों (transformations) ______ _______ __________ ____ _________.
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