Question
प्राचल विचरण विधि द्वारा समीकरण$
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Answer :
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हम समीकरण [ \frac{d^2y}{dx^2} + a^2 y = \sec(ax) ] को प्राचल विचरण विधि (Variation of Parameters) द्वारा हल करेंगे। सबसे पहले इसे हल करने की प्रक्रिया शुरू करते हैं। 1. सम्बंधित सममित समीकरण का हल (Homogeneous solution): संबंधित सममित समीकरण है: [ \frac{d^2y}{dx^2} + a^2 y = 0 ] इसका विशेषता समीकरण है: [ r^2 + a^2 = 0 \implies r = \pm ai ] अतः सममित हल है: [ y_h = C_1 \cos(ax) + C_2 \sin(ax) ] 2. प्राचल विचरण के लिए विधि: यदि (y_1 = \cos(ax)) और (y_2 =
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