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Solve the following ordinary differential equations:
(i)
(ii)
दिखायें कि फलन
एक-विमिय ताप समीकरण का हल है।
निम्नलिखित आदि मान समस्या को हल करें :
Show that:
is a solution of the one-dimensional heat equation.
A parachutist is falling with a speed of when his parachute opens. If the air resistance is (Mv2)/25 where M is the total mass of the man and his parachute, find the speed of the man as a function of time t after the parachute opens. Take
.
व्यास वाला एक बेलन पानी में ऐसे खड़ा है कि उसका अक्ष ऊर्ध्वाधर दिशा में है। जब उसे थोड़ा सा दबाकर छोड़ दिया जाता है, वह
की आवर्तकाल के साथ दोलन करता है। बेलन का द्रव्यमान प्राप्त करें।
The surface of a ball of radius A is kept at a temperature zero. If the initial temperature in the ball is f(r), write down the boundary conditions and show that the temperature in the ball at time t, u(r, t), is the solution to the equation: