Ch 9 introduces differential equations — equations involving derivatives. Students learn to classify DEs by order and degree, form DEs from given functions, and solve them using various methods.
Order: the order of the highest derivative. Degree: the power of the highest-order derivative (if polynomial in derivatives). Example: (d²y/dx²)³ + (dy/dx)² = x has order 2, degree 3.
Variable separable: rearrange as f(x)dx = g(y)dy, integrate both sides. Homogeneous: substitute y = vx, reduces to variable separable. Linear (first order): dy/dx + P(x)y = Q(x), solution uses integrating factor e^(∫Pdx).
Download: https://ncert.nic.in/textbook/pdf/lemh203.pdf | Complete book Part II: https://ncert.nic.in/textbook/pdf/lemh2ps.zip
For a linear DE dy/dx + Py = Q: multiply both sides by IF = e^(∫Pdx). The left side becomes d/dx(y·IF). Integrate both sides: y·IF = ∫Q·IF dx + C. This works because the IF makes the left side an exact derivative.
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